The DOI matches its Crossref record; 69 of the 70 references it cites were found in a registry or an index; none of the 16 sources its claims cite is checked for support yet.
Accelerated quantum walk, two-particle entanglement generation and localization
Open accessAbstract
We present a scheme to describe the dynamics of accelerating discrete-time quantum walk for one- and two-particle in position space. We show the effect of acceleration in enhancing the entanglement between the particle and position space in one-particle quantum walk and in generation of entanglement between the two unentangled particle in two-particle quantum walk. By introducing the disorder in the form of phase operator we study the transition from localization to delocalization as a function of acceleration. These inter-winding connection between acceleration, entanglement generation and localization along with well established connection of quantum walks with Dirac equation can be used to probe further in the direction of understanding the connection between acceleration, mass and entanglement in relativistic quantum mechanics and quantum field theory. Expansion of operational tools for quantum simulations and for modelling quantum dynamics of accelerated particle using quantum walks is an other direction where these results can play an important role.
Overview
AI snapshot
Written from the paper’s full text.
TL;DR
The paper introduces acceleration into discrete-time quantum walks by making the coin parameter time-dependent as θ(a,t)=θ₀e⁻ᵃᵗ, and studies single- and two-particle dynamics, entanglement, and disorder-induced localization. It reports that acceleration increases position-space spreading and particle–position entanglement, can entangle initially unentangled two particles, and drives a transition from localization to delocalization as acceleration increases.
Key findings
- For single-particle accelerated walks, increasing a increases the spread in position space; standard deviation σ increases with a until it reaches a maximum bounded by σ=t, while θ₀ sets the minimum spread. Negativity between particle and position space increases with a and with steps, reaching the maximum value 0.5 faster for larger a.
- For two-particle walks with initial state |↑↑⟩⊗|x=0⟩⊗|y=0⟩, acceleration increases the probability spread. For θ₀=π/2, a=0 produces no entanglement between the two particles; small a generates entanglement that fades after long evolution, and larger a decreases the generated entanglement and makes it fade faster. For θ₀=π/4, a=0 makes the coin operator entangle the particles instantaneously and remain entangled, while increasing a makes this entanglement fade faster.
- With disorder introduced via a random phase operator, spatial disorder (random φₓ) and temporal disorder (random φₜ) produce localization for small a, but as a increases the accelerated coin operator dominates and the walk delocalizes. Entanglement between the two particles decays faster for delocalized/higher-a cases, while spatial localized accelerated walks preserve entanglement longer than the no-disorder accelerated walk.
- The two-particle interacting coin is equivalent to an Ising Hamiltonian H=σₓ⊗σₓ, and the quantum-walk mapping to the Dirac equation gives m∝sin(θ) and c∝cos(θ); small a corresponds to larger mass, slower spread, and higher entanglement generation.
Methods
- Theoretical and numerical study of discrete-time quantum walks with coin C(θ₀), position shift S, and acceleration via θ(a,t)=θ₀e⁻ᵃᵗ. Single-particle walks are in one dimension; two-particle walks use an interacting coin Cθ₀=cos(θ₀)(I₂⊗I₂)−i sin(θ₀)(σₓ⊗σₓ) followed by a two-dimensional shift S(x,y).
- Disorder is introduced by a phase operator Φ(φ) with random φₓ for spatial disorder or random φₜ for temporal disorder, each drawn from 0≤φ≤π. The analysis uses dispersion relations, transfer matrices, and numerical simulations, with negativity used to quantify entanglement.
- Initial states include single-particle |Ψin⟩=(α|↑⟩+β|↓⟩)⊗|x=0⟩, often 1/√2(|↑⟩+|↓⟩), and two-particle |↑↑⟩⊗|x=0⟩⊗|y=0⟩. Parameters shown include θ₀=π/4 and π/2, a=0, 0.002, 0.02, 0.2, steps up to 200, 400, and 500, and disorder averages over 500 or 1000 runs.
Limitations
- Stated in the paper: more analytical studies are still required to explicitly formalize some observations related to entanglement behavior in systems with more than two particles.
- Stated in the paper: the two-particle dynamics is restricted to one-dimensional position space due to the bosonic/fermionic nature of the chosen initial state and operators.
- Evident from the text: the results rely on numerical simulations for finite steps and specific initial states, θ₀ values, and acceleration parameters; no experimental realization is reported.
Model-written summary. Check it against the paper before relying on it.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
0 of 16 cited sources checked · 0 supported · 0 flagged
- Findingreasoning
For two-particle accelerated quantum walk with temporal disorder, higher a leads to particle delocalization.
“Higher the value of a, the particle delocalizes which implies that at higher value of a the interaction coin operator dominates over the phase operator which is similar to the spatial disordered and singleparticle case.”
Quote in the paperSubstantial claim - Findingreasoning
For accelerated single-particle quantum walk, increasing the acceleration increases the spread of the probability amplitude in position space.
“As the value of a increases, the spread in the position space increases.”
Quote in the paperSubstantial claim - Findingnone given
Introducing disorder in the form of a phase operator produces a transition from localization to delocalization as a function of acceleration.
“By introducing the disorder in the form of phase operator we study the transition from localization to delocalization as a function of acceleration.”
Quote in the paperSubstantial claim - Findingown data
In the two-particle accelerated quantum walk, as acceleration increases, the spread of the probability amplitude in position space increases.
“Fig. 9 shows the probability distribution of the two-particle accelerated quantum walk with different values of acceleration parameter a and as the acceleration in the system increases the spread of the probability amplitude in position space also increases.”
Quote in the paperSubstantial claim - Findingown data
For non-accelerated two-particle quantum walk (a = 0) with θ0 = π/2, no entanglement is generated between the two particles.
“For non-accelerated quantum walk (a = 0) when θ 0 = π/2 we do not see any entanglement being generated between the two particles.”
Quote in the paperSubstantial claim
- Findingown data
With increase in both acceleration a and time t simultaneously, entanglement between the two particles fades off faster with time.
“With increase in both a and t simultaneously, entanglement fades off faster with time.”
Quote in the paperSubstantial claim - Findingnone given
For the configuration |↑↑, the probability amplitude spreading of the two particles evolves together just like a single-particle quantum walk.
“For this configuration we can note that the probability amplitude spreading of two-particles will evolve together just like a single-particle quantum walk.”
Quote in the paperSubstantial claim - Findingreasoning
For two-particle accelerated discrete-time quantum walk with coin parameter θ0 and φ at all sites, the dispersion relation between ψ↑↓ and ψ↓↑ is cos(φ + ω) = cos(θ0) cos(κ2).
“Similarly, the dispersion relation between ψ ↑↓ and ψ ↓↑ for two-particle when coin parameter at all sites is θ 0 and φ is given by, cos(φ + ω) = cos(θ 0 ) cos(κ 2 ).”
Quote in the paperSubstantial claim - Findingown data
Acceleration generates entanglement between two initially unentangled particles in two-particle discrete-time quantum walk.
“and in generation of entanglement between the two unentangled particle in two-particle quantum walk.”
- Also stated in: § I. INTRODUCTION · plain
“present the situations where acceleration plays a role in entangling the two initially unentangled particles.”
Quote in the paperSubstantial claim- Rests on an assumption: The results obtained for the initial two-particle state |↑↑ also hold for the initial two-particle state |↑↓.
- Also stated in: § I. INTRODUCTION · plain
- Findingreasoning
If the initial two-particle state is |↑↑ or |↑↓, the state after t steps evolves only in a configuration of two basis states and one-dimensional space.
“If the initial state of the two particle is in one of the basis states | ↑↑ ⊗ |x = 0 ⊗ |y = 0 or | ↑↓ ⊗ |x = 0 ⊗ |y = 0 the state after t step will evolve only in configuration of two of the basis states and one-dimensional space,”
Quote in the paperSubstantial claim - Findingnone given
For disordered two-particle accelerated quantum walk, the decay time is lower as acceleration decreases.
“Similarly, for disordered two-particle accelerated quantum walk, the decay time is lower as we decrease the acceleration.”
Quote in the paperSubstantial claim - Findingown data
Entanglement decays faster for two-particle accelerated quantum walk without disorder compared to walk with spatial and temporal disordered system in one dimension.
“Entanglement decays faster for two-particle accelerated quantum walk without disorder when compared to walk with spatial and temporal disordered system in one dimension as shown in Figs.21 and 22.”
Quote in the paperSubstantial claim - Findingreasoning
For two-particle accelerated quantum walk with spatial disorder, higher values of a lead to particle delocalization.
“Higher the value of a, the particle delocalizes which implies that at higher value of a the interaction operator C θ with θ = θ 0 e -at dominates over the phase operator in coin operation.”
Quote in the paperSubstantial claim - Findingown data
For an accelerated two-particle walker with θ0 = π/4, there is no noticeable increase in entanglement between the two-particle and position space compared to quantum walk without acceleration.
“However, for an accelerated walker with an offset θ 0 = π/4 (θ 0 < π/2) the value of cos(θ(a, t)) increase with a small gradient and the effect of acceleration does not last long in the dynamics.Therefore, we don't see any noticeable increase in entanglement when compared to quantum walk without acceleration.”
Quote in the paperSubstantial claim - Findingreasoning
For the evolution operator with phase, the group velocity depends on both evolution parameters θ0 and φ.
“and it implies that for evolution operator with phase, the group velocity depends upon both, the evolution parameters θ 0 and φ.”
Quote in the paperNot a substantial claim - Findingown data
For two-particle accelerated quantum walk, the decay time of entanglement between the particles is lower as acceleration increases.
“The decay time is lower as we increase the acceleration.”
Quote in the paperSubstantial claim - Findingown data
For single-particle accelerated quantum walk with temporal disorder, as the acceleration parameter a increases, the particle delocalizes in position space.
“As the value of a increases, the particle delocalizes in position space which implies that the interacting coin operator dominates over the phase operator.”
Quote in the paperSubstantial claim - Findingreasoning
The two-particle quantum walk described in this section reproduces dynamics identical to the single-particle quantum walk.
“Our choice of initial state and interacting coin operation in this subsection on two-particle quantum walks reproduces the dynamics identical to the single-particle quantum walk.”
Quote in the paperSubstantial claim - Findingown data
For accelerated single-particle quantum walk, negativity between the particle and position space increases with acceleration and with number of steps until it reaches a maximum value.
“In general, one can see a significant increase in negativity with increase in acceleration and with increase in number of steps (time) until it reaches a maximum value.”
- Also stated in: § II. ACCELERATED DISCRETE-TIME QUANTUM WALK A. Single-particle · plain
“For an accelerated quantum walk we can see a study increase in negativity with increase in number of steps.”
Quote in the paperSubstantial claim - Also stated in: § II. ACCELERATED DISCRETE-TIME QUANTUM WALK A. Single-particle · plain
- Findingreasoning
For two-particle accelerated discrete-time quantum walk with coin parameter θ0 and φ at all sites, the dispersion relation between ψ↑↑ and ψ↓↓ is cos(ω + φ) = cos(θ0) cos(φ + κ1).
“the dispersion relation between the ψ ↑↑ and ψ ↓↓ for the given evolution operator when coin parameter at all sites is θ 0 and φ for two-particle accelerated discrete-time quantum walk is given by, cos(ω + φ) = cos(θ 0 ) cos(φ + κ 1 ).”
Quote in the paperSubstantial claim - Findingreasoning
Entanglement between position and particle in single-particle quantum walk reaches its maximum value faster with increase in acceleration and then saturates at the maximum value.
“Entanglement between the position and particle in the single-particle quantum walk reaches its maximum value faster with increase in acceleration and then saturates at the maximum value.”
Quote in the paperSubstantial claim - Findingown data
For a = 0, the negativity between the particle and position space oscillates between maximum and minimum values.
“For a = 0 we will only see the oscillation between the maximum and minimum values.”
Quote in the paperNot a substantial claim - Findingown data
For larger a, entanglement between coin and position Hilbert space reaches maximum value faster in time.
“For larger a entanglement reaches maximum value faster in time.”
Quote in the paperSubstantial claim - Findingnone given
For the two-particle case, acceleration in the system spreads the probability amplitude faster in position space.
“For the two-particle case also the acceleration in the system spreads the probability amplitude faster in position space.”
Quote in the paperSubstantial claim - Findingown data
The spread is always maximum even when compared to the delocalized distribution with disorder.
“The spread is always maximum even when compared to the delocalized distribution with disorder.”
Quote in the paperNot a substantial claim - Findingown data
Entanglement between coin and position Hilbert space H_py is zero for the given initial state because the probability distribution in this Hilbert space is zero.
“Entanglement between coin and position Hilbert space Hp y is zero as the probability distribution in this Hilbert space is zero for the given initial state.”
Quote in the paperNot a substantial claim - Findingown data
When acceleration dominates over disorder, the probability distribution delocalizes for both spatial and temporal disorder.
“When acceleration dominates over disorder the probability distribution delocalizes for both, spatial and temporal disorder.”
Quote in the paperSubstantial claim - Findingnone given
For a single-particle quantum walk, introduction of acceleration increases the rate of spread of the probability amplitude over position space.
“For a single-particle quantum walk, introduction of acceleration into the system increases the rate of spread of the probability amplitude over the position space.”
Quote in the paperSubstantial claim - Findingown data
Spatial disorder for small a shows strong localization compared to temporal disorder.
“Spatial disorder for small value of a shows a strong localization compared to the temporal disorder.”
Quote in the paperSubstantial claim - Findingown data
With increase in acceleration a, the instantaneous entanglement generated between the two particles fades off faster, dis-entangling them.
“However, with increase in a the instantaneous entanglement generated fades off faster dis-entangling the two particles.”
Quote in the paperSubstantial claim - Findingown data
The entanglement for the delocalized case decays faster than the localized case in two-particle accelerated quantum walk with spatial and temporal disorder.
“The entanglement for the delocalized case decays faster then the localized case in two-particle accelerated quantum walk with spatial and temporal disorder.”
Quote in the paperSubstantial claim - Findingown data
For higher acceleration a, cos(θ0 e^{-at}) reaches unity very early in time.
“For higher value of a we can see cos(θ 0 e -at ) reaching unity very early in time.”
Quote in the paperSubstantial claim - Findingown data
Acceleration enhances the entanglement between the particle and position space in one-particle discrete-time quantum walk.
“We show the effect of acceleration in enhancing the entanglement between the particle and position space in one-particle quantum walk”
- Also stated in: § I. INTRODUCTION · plain
“we observe some interesting features like enhancement in the quantity of entanglement between the particle and position space as a function of acceleration in one-dimensional single-particle quantum walk.”
Quote in the paperSubstantial claim - Also stated in: § I. INTRODUCTION · plain
- Findingreasoning
In two-particle discrete-time quantum walk, coin states |↑↑> and |↓↓> evolve particles in the x-direction and coin states |↑↓> and |↓↑> evolve particles in the y-direction in two dimensions when the initial state is symmetric or same.
“The expression for state of two-particle discrete-time quantum walk shows that coin state | ↑↑ and | ↓↓ will evolve the particles in x-direction and coin state | ↑↓ and | ↓↑ will evolve the particles in y-direction in two-dimension when the initial state of the particle is symmetric or same.”
Quote in the paperSubstantial claim - Findingown data
For smaller acceleration a, negativity between the particle and position space increases very slowly as a function of the number of steps.
“For smaller value of a, a very slow increase in negativity as function of number of steps is seen.”
Quote in the paperNot a substantial claim - Interpretationreasoning
The above formulation can be written in one-dimensional position space when the initial state in coin space is one of the four basis states.
“Therefore, above formulation can be written in one-dimensional position space when the initial state in coin space is one of the four basis state.”
Quote in the paperNot a substantial claim - Interpretationown data
Entanglement between the particle and position space in two-particle accelerated walk shows similar characteristics as single-particle accelerated walk in one dimension.
“Entanglement between the particle and position space shows similar characteristic as single-particle accelerated walk in one dimension.”
Quote in the paperSubstantial claim - Interpretationown data
A gradient in acceleration before it saturates to its maximum value plays an important role in generation of maximum entanglement between the two-particle and position space.
“Heuristically we can say that a gradient in acceleration before it is saturated to maximum value plays an important role in generation of maximum entanglement between the twoparticle and the position space.”
Quote in the paperSubstantial claim - Interpretationown data
The greater the spread in position space, the faster the death of entanglement between particles evolving in position space.
“Maximum the spread in the position space faster is the death of the entanglement between the particles evolving in position space.”
Quote in the paperSubstantial claim - Interpretationcitation
The increase in entanglement seen with time-dependent coin operation causing acceleration allies well with earlier results of increase in entanglement between particle and position space due to random coin operation for each time.
“The increase in entanglement seen with time dependent coin operation causing acceleration allies well with the earlier results of increase in entanglement between particle and position space due to random coin operation for each time [26,58].”
Quote in the paperNot a substantial claim0 of 2 sources checked- cites [26]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- cites [58]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Interpretationreasoning
For single-particle accelerated quantum walk with temporal disorder, as a increases, the interacting coin operator dominates over the phase operator.
“As the value of a increases, the particle delocalizes in position space which implies that the interacting coin operator dominates over the phase operator.”
Quote in the paperSubstantial claim - Premisecitation
Parameter θ in the quantum walk coin operation or in operations describing Dirac cellular automata is mapped to the mass and velocity of a Dirac particle as m ∝ sin(θ) and c ∝ cos(θ).
“Parameter θ in the quantum walk coin operation or in the operations that describe Dirac cellular automata has been effectively mapped to the mass and velocity of Dirac particle, that is, m ∝ sin(θ) and c ∝ cos(θ).”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [4,[37][38][39][40][41][42][43]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Interpretationreasoning
For two-particle accelerated quantum walk with temporal disorder, at higher a the interaction coin operator dominates over the phase operator, similar to spatial disordered and single-particle cases.
“Higher the value of a, the particle delocalizes which implies that at higher value of a the interaction coin operator dominates over the phase operator which is similar to the spatial disordered and singleparticle case.”
Quote in the paperSubstantial claim - Interpretationreasoning
The accelerated two-particle quantum walk is similar to the Ising model with perturbed Ising model.
“The accelerated twoparticle quantum walk is similar to the Ising model with perturbed Ising model.”
Quote in the paperNot a substantial claim - Interpretationreasoning
The enhancement of quantum correlation (negativity or entanglement entropy) in quantum walks is generally due to the time-dependent quantum coin operation and not due to a specific effect of randomness in time.
“Thus, one can say that the enhancement of quantum correlation (negativity or entanglement entropy) is in general due to the time dependent quantum coin operation and not due to a specific effect of randomness in time.”
Quote in the paperSubstantial claim0 of 2 sources checked- cites [26]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- cites [58]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Interpretationreasoning
Acceleration to quantum walk dynamics can be introduced by any time-dependent function of the coin parameter that contributes a change in group velocity with time.
“Therefore, acceleration to quantum walk dynamics can be introduced any time dependent function of coin parameter which contributes change in group velocity with time.”
Quote in the paperSubstantial claim - Interpretationreasoning
When θ is a function of a and t, a small value of a corresponds to a larger mass of the particle.
“When θ is a function of a and t we see that small value of a corresponds to larger mass of the particle.”
Quote in the paperSubstantial claim - Interpretationreasoning
For two-particle accelerated quantum walk with spatial disorder, at higher a the interaction operator Cθ with θ=θ0 e^{-at} dominates over the phase operator in coin operation.
“Higher the value of a, the particle delocalizes which implies that at higher value of a the interaction operator C θ with θ = θ 0 e -at dominates over the phase operator in coin operation.”
Quote in the paperSubstantial claim - Interpretationown data
The behavior of single-particle accelerated quantum walk with temporal disorder is similar to the spatial disordered case.
“A similar behaviour as seen for spatial disordered case.”
Quote in the paperNot a substantial claim - Interpretationcitation
The increase in negativity with time-dependent coin operation causing acceleration allies with earlier results of increase in entanglement between particle and position space due to random coin operation for each time.
“The increase in negativity seen with time dependent coin operation causing acceleration allies well with the earlier results of increase in entanglement between particle and position space due to random coin operation for each time [26,58].”
Quote in the paperSubstantial claim0 of 2 sources checked- cites [26]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- cites [58]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Interpretationreasoning
The entanglement between interacting particles stays for a longer time when the value of acceleration is smaller compared to higher acceleration for which the particle is delocalized.
“This implies that the entanglement between the interacting particles stays for a longer time when the value of acceleration is smaller when compared to higher value of acceleration for which the particle is delocalized.”
Quote in the paperSubstantial claim
- It may state two separate claims as one. 28
- The quote only partly states this claim. 1
- Probably not a substantial claim. 7
It may state two separate claims as one.
Findingown dataWith increase in acceleration a, the entanglement generated between the two particles decreases and fades off faster with time.
“With increase in a, entanglement generated decreases and fades off faster with time.”
Quote in the paperSubstantial claimThe quote only partly states this claim.
Findingnone givenThe spread of the probability distribution is always wider in the absence of disorder than in the presence of disorder.
“However, spread of the distribution is always wider in absence of disorder when compared configuration of leading to deloclization in presence of disorder.”
Quote in the paperNot a substantial claimIt may state two separate claims as one.
Findingnone givenFor higher a, particles reach maximum entanglement in short time for standard accelerated quantum walk as well as for disordered quantum walk and remains constant with time.
“Similar to single-particle accelerated quantum walk, for higher value of a particle reaches the maximum entanglement in short time for standard accelerated quantum walk as well as for disordered quantum walk and re-mains constant with time.”
Quote in the paperSubstantial claimIt may state two separate claims as one.
FindingreasoningFor two-particle accelerated discrete-time quantum walk, given the coin operator, ψ↑↑ and ψ↓↓ evolve in superposition of ψ↑↑ and ψ↓↓, and ψ↑↓ and ψ↓↑ evolve in superposition of ψ↑↓ and ψ↓↑.
“From the Eqs.(34)(35)(36)(37), it is clear that given coin operator ψ ↑↑ and ψ ↓↓ evolves in superposition of ψ ↑↑ and ψ ↓↓ and similarly, ψ ↑↓ and ψ ↓↑ in superposition of ψ ↑↓ and ψ ↓↑ , respectively as it was discussed for evolutions without phase operator.”
Quote in the paperSubstantial claimIt may state two separate claims as one.
Findingnone givenIn accelerated quantum walk, the same maximum spread as in a regular quantum walk is achieved along with interference effect.
“But in accelerated quantum walk same maximum spread is achieved along with interference effect.”
Quote in the paperSubstantial claim- Rests on an assumption: In a regular quantum walk, maximum spread is achieved only when θ0 → 0, and this happens without any interference of the particle in position space.
It may state two separate claims as one.
Findingown dataFor the initial state |↑↑> ⊗ |x=0> ⊗ |y=0>, evolution in H_py is zero, so the two-particle quantum walk study reduces to one dimension.
“For further study of two particle quantum walk, we will analyse the initial state | ↑↑ ⊗ |x = 0 ⊗ |y = 0 therefore the study reduces to one-dimension as evolution in H py is zero for the given initial state.”
Quote in the paperSubstantial claimIt may state two separate claims as one.
FindingreasoningMaximum entanglement between particles is found in the accelerated quantum walk, but entanglement stays for longer time for spatial localized accelerated quantum walk.
“It can be seen that maximum entanglement between the particle is found in the accelerated quantum walk but entanglement stays for longer time for spatial localized accelerated quantum walk.”
Quote in the paperSubstantial claimIt may state two separate claims as one.
Findingown dataFor higher acceleration a, negativity between the particle and position space increases with number of steps, quickly reaches a maximum value, and remains maximum with further increase in steps.
“For higher value of a, negativity increases with number of steps and quickly reaches a maximum value and remains maximum with further increase in steps.”
Quote in the paperSubstantial claimIt may state two separate claims as one.
Findingown dataFor θ0 = π/4 and a = 0, the coin operator itself acts as an entangling operator, entangling the two particles instantaneously, and they remain entangled.
“When the offset of θ(a, t) is set with θ 0 = π/4 and a = 0 the coin operator Eq. 12 itself will acts as an entangling operator and it entangles the two particles instantaneously and remains entangled.”
Quote in the paperSubstantial claimIt may state two separate claims as one.
FindingreasoningFor both spatial and temporal disordered quantum walk with acceleration, the entanglement between the two particles increases with acceleration, reaches the maximum entanglement value faster, and decays faster in time.
“For both, spatial and temporal disordered quantum walk with acceleration, the entanglement between the two particles increase with acceleration, reaches the maximum entanglement value faster and decays faster too in time.”
Quote in the paperSubstantial claimIt may state two separate claims as one.
FindingreasoningIntroducing disorder in either coin parameter θx or φx leads to spatial and temporal disorder, respectively.
“Eqs. (40) and (33) shows that introducing disorder in either of the coin parameter θ x or φ x will lead to spatial and temporal disorder, respectively.”
Quote in the paperSubstantial claimIt may state two separate claims as one.
Findingown dataFor an accelerated two-particle walker with θ0 = π/2, negativity between the two-particle and position space increases with time, and the maximum negativity is reached by a walker with higher acceleration a.
“For an accelerated walker for any value a when cos(θ(a, t)) goes from 0 to 1 with time t (θ 0 = π/2) we see an increase in negativity with time and maximum value of negativity is reached by an walker with higher value of a.”
Quote in the paperSubstantial claimIt may state two separate claims as one.
Findingown dataFor small acceleration a, entanglement is generated between the two particles and after a long time evolution it fades off.
“However, for small value of a we can notice generation of entanglement between the two particles and after a long time evolution it fades off.”
Quote in the paperSubstantial claimIt may state two separate claims as one.
Findingown dataFor single-particle accelerated quantum walk, the standard deviation σ increases significantly with acceleration a until it reaches a maximum spread bounded by σ = t, with θ0 setting the minimum σ.
“A significant increase in σ with increase in a is seen until it attains a maximum spread bounded by σ = t and θ 0 sets the minimum σ.”
Quote in the paperSubstantial claimIt may state two separate claims as one.
Findingown dataFor a = 0.002 when the particle is localized, entanglement decays faster but reaches its maximum value slower compared to the delocalized case when a = 0.02.
“For a = 0.002 when the particle is localized, entanglement decays faster but entanglement reaches to its maximum value slower in localized case when compared to delocalized case when a = 0.02.”
Quote in the paperSubstantial claimIt may state two separate claims as one.
FindingreasoningIn a standard quantum walk without acceleration with disorder, localization is seen, but in accelerated quantum walk with disorder localization is seen only when acceleration is very small.
“In a standard quantum walk (without acceleration) with disorder we will see localization but in accelerated quantum walk with disorder localization is seen only when the acceleration is very small.”
Quote in the paperSubstantial claim- Rests on an assumption: In a standard quantum walk without acceleration with disorder, localization is seen.
It may state two separate claims as one.
Findingown dataFor a single-particle quantum walk, acceleration results in enhancement of entanglement between the particle and position space and reaches a maximum value in shorter time.
“It also results in enhancement of entanglement between the particle and the position space and reaches a maximum value in shorter time.”
Quote in the paperSubstantial claimIt may state two separate claims as one.
Findingown dataFor extremely small acceleration a, entanglement between the two particles picks up slowly and remains entangled with time.
“for extremely small value of a the entanglement between the two particles picks up slowly and will remain entangled with time.”
Quote in the paperSubstantial claimIt may state two separate claims as one.
Findingown dataFor the two-particle discrete-time quantum walk, the probability distribution in the x-direction and y-direction are independent of each other and depend on the initial coin state.
“We can see that the probability distribution in x-direction and ydirection are independent of each other and are dependent on initial coin state.”
Quote in the paperSubstantial claimProbably not a substantial claim. The paper may give no reason why it holds.
Interpretationnone givenThe results are in general valid for any time-dependent function of the coin parameter that introduces acceleration into the dynamics.
“These results are in general valid for any time dependent function of coin parameter which introduces acceleration into the dynamics.”
Quote in the paperNot a substantial claimIt may state two separate claims as one.
InterpretationreasoningThe enhancement of entanglement is in general due to the time-dependent quantum coin operation, and enhancement due to randomness in time is a specific case.
“Thus, one can corroborate that the enhancement of entanglement is in general due to the time dependent quantum coin operation and enhancement due to randomness in time is a specific case.”
Quote in the paperSubstantial claimIt may state two separate claims as one.
PremisecitationFor any value of θ between the limiting values, interference effects play an important role and the spread of the probability distribution of the walker after t steps is bounded between ±t cos(θ0).
“For any value of θ between these values, interference effects plays an important role and the spread of the probability distribution of the walker after t steps of walk will be bounded between ±t cos(θ 0 ) [7,18]”
Quote in the paperSubstantial claim0 of 2 sources checked- cites [7]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- cites [18]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
It may state two separate claims as one.
Interpretationown dataIn single-particle accelerated quantum walk with spatial disorder in the phase parameter, the particle delocalizes for higher acceleration a, implying that the θ operator saturating at maximum velocity dominates over the random phase operator.
“Particle delocalizes for higher value of a implying that θ operator which saturates at maximum velocity θ(a, t) → 0 dominates over the random phase operator.”
Quote in the paperSubstantial claimIt may state two separate claims as one.
Interpretationown dataAs acceleration in the system increases, particles in position space delocalize because the entangling operator dominates over the phase operator.
“As the acceleration in the system increases, the particles in position space delocalizes as the entangling operator dominates over the phase operator.”
Quote in the paperSubstantial claimIt may state two separate claims as one.
Interpretationnone givenThe increase in standard deviation with acceleration happens because the quantum coin operation transitions towards the identity operator with time, and for higher a the coin evolution operator tends towards identity faster.
“Increase in standard deviation with acceleration happens due to the transition of quantum coin operation towards identity operator with time and for higher value a coin evolution operator tends towards identity faster.”
Quote in the paperSubstantial claimProbably not a substantial claim. The paper’s conclusions may not depend on it.
PremisecitationDisorder in discrete-time quantum walk has been studied by replacing θ0 in the quantum coin operation with a random value 0 ≤ θj ≤ π in position or time.
“Disorder in discrete-time quantum walk has been studied by replacing θ 0 in the quantum coin operation with a random value 0 ≤ θ j ≤ π in position (j = x) or time (j = t) [26,49,50].”
Quote in the paperNot a substantial claim0 of 3 sources checked- cites [26]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- cites [49]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- cites [50]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Probably not a substantial claim.
PremisecitationIn an alternative approach, disorder has been introduced in the form of a random phase operation along with the coin operation with fixed θ0.
“In an alternative approach, disorder has been introduced in the form of random phase operation along with the coin operation with fixed θ 0 [47,48].”
Quote in the paperSubstantial claim0 of 2 sources checked- cites [47]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- cites [48]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
It may state two separate claims as one.
InterpretationreasoningAs acceleration increases, the system becomes delocalized because the increase in acceleration increases the perturbation in the unitary operator and that dominates over the disordered phase parameter.
“As acceleration increases the system becomes delocalized because, the increase in acceleration increases the perturbation in the unitary operator and that dominates over the disordered phase parameter in the system.”
Quote in the paperSubstantial claimIt may state two separate claims as one.
InterpretationreasoningHigher mass corresponds to slower spread and higher entanglement generation.
“Thus, higher the mass, slower is the spread and higher is the entanglement generation.”
Quote in the paperSubstantial claimProbably not a substantial claim. The paper’s conclusions may not depend on it.
PremisecitationThe interacting coin operator used in the two-particle dynamics, without acceleration parameter, is equivalent in Hamiltonian form to the Ising model Hamiltonian H = σx ⊗ σx, which is a special case of the generalized Heisenberg model.
“The interacting coin operator we have used in our two particle dynamics without acceleration parameter in its Hamiltonian form is equivalent to the Hamiltonian of Ising model which is a special case of generalised Heisenberg model [45,46].”
Quote in the paperNot a substantial claim0 of 2 sources checked- cites [45]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- cites [46]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
It may state two separate claims as one.
InterpretationreasoningThe parameter a in the coin operation induces acceleration to the dynamics, where the minimum spread is bounded by θ0 and the maximum spread is achieved with time for any small a > 0.
“The parameter a in the coin operation induces acceleration to the dynamics where the minimum spread will be bounded by the value of θ 0 and maximum spread will be achieved with time for any small value of a > 0 (θ → 0).”
Quote in the paperSubstantial claimIt may state two separate claims as one.
InterpretationreasoningWith a > 0, a particle that spreads in position space localizes the two states |↑ and |↓ to bimodal form and moves away from each other.
“This implies that with a > 0 a particle which spreads in position space localizes the two states | ↑ and | ↓ to bimodal form and move away from each other.”
Quote in the paperSubstantial claimProbably not a substantial claim. The paper may give no reason why it holds.
Interpretationnone givenThe chosen initial state and choice of coin and shift operator ensure the fermionic and bosonic nature of the wave function by introducing symmetry and anti-symmetry in the spin state.
“This initial state and the choice of coin and shift operator we have chosen ensures the fermionic and bosonic nature of the wave function as the symmetry and anti-symmetry is introduced in the spin state.”
Quote in the paperNot a substantial claimProbably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds. It may state two separate claims as one.
Interpretationnone givenThe two-particle quantum walk system in this paper is similar to the condensed matter Ising model, which is a special case of the Heisenberg model.
“The two-particle quantum walk system in this paper is sim-ilar to the condensed matter Ising model with is a special case of Heisenberg model.”
Quote in the paperNot a substantial claimProbably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
Interpretationnone givenThe superposition and interference between the particles' wave function in two-particle accelerated quantum walk is more than the interference effect in localized discrete-time quantum walk.
“It could be because the superposition and interference between the particles wave function in two-particle accelerated quantum walk is more than the interference effect in localized discrete-time quantum walk.”
Quote in the paperNot a substantial claim
The paper relies on this without support.
The results obtained for the initial two-particle state |↑↑ also hold for the initial two-particle state |↑↓.
“and this should hold good even for the initial two particle state | ↑↓ .”
The paper relies on this without support.
In a regular quantum walk, maximum spread is achieved only when θ0 → 0, and this happens without any interference of the particle in position space.
“In a regular quantum walk the maximum spread is achieved only when θ 0 → 0 but that happen without any interference of the particle in position space.”
The paper relies on this without support.
Randomizing φ at each position in position space gives Anderson localization, and randomizing φ at each step gives weak localization.
“randomizing φ at each position in the position space gives Anderson localization and randomizing φ at each step in the position space gives weak localization.”
The paper relies on this without support.
In a standard quantum walk without acceleration with disorder, localization is seen.
“In a standard quantum walk (without acceleration) with disorder we will see localization but in accelerated quantum walk with disorder localization is seen only when the acceleration is very small.”
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Localized case is said to decay both slower and faster
MinorThe passage first says entanglement decays faster in the delocalized case than in the localized case, then says it decays faster for the localized a=0.002 case than for the delocalized a=0.02 case.
“The entanglement for the delocalized case decays faster then the localized case in two-particle accelerated quantum walk with spatial and temporal disorder.”
“For a = 0.002 when the particle is localized, entanglement decays faster but entanglement reaches to its maximum value slower in localized case when compared to delocalized case when a = 0.02.”
Ising Hamiltonian drops a factor of two
MinorSubstituting the stated γ=1 and N=2 into Eq. (44) leaves one x-direction interaction with coefficient 1+γ=2. Eq. (45) gives the same interaction with coefficient 1, without stating a rescaling.
“therefore γ = 1 and since its a two-particle interaction therefore N = 2 and hence the Hamiltonian for two-particle quantum walk is given by, H = S x 1 ⊗ S x 2 ,(45)”
“H γ = N -1 i (1 + γ)(S x i ⊗ S x i+1 ) + (1 -γ){(S y i ⊗ S y i+1 ) + (S z i ⊗ S z i+1 )}(44)”
Citations
Cites
Absence of Diffusion in Certain Random Lattices
Anderson, P. W. (1958) · Physical Review · doi:10.1103/physrev.109.1492 · Cited by 12,468
Lee, P. A., & Ramakrishnan, T. V. (1985) · Reviews of Modern Physics · doi:10.1103/revmodphys.57.287 · Cited by 6,123
Two soluble models of an antiferromagnetic chain
Lieb, É. H., Schultz, T. D., & Mattis, D. C. (1961) · Annals of Physics · doi:10.1016/0003-4916(61)90115-4 · Cited by 4,292
Entanglement in many-body systems
Amico, L., Fazio, R., Osterloh, A., & Vedral, V. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.517 · Cited by 3,745
Pollak, M., Ortuño, M., & Frydman, A. (2012) · Cambridge University Press eBooks · doi:10.1017/cbo9780511978999.002 · Cited by 3,420
Classification of topological insulators and superconductors in three spatial dimensions
Schnyder, A. P., Ryu, S., Furusaki, A., & Ludwig, A. W. W. (2008) · Physical Review B · doi:10.1103/physrevb.78.195125 · Cited by 3,322
Weak localization in thin films
Bergmann, G. (1984) · Physics Reports · doi:10.1016/0370-1573(84)90103-0 · Cited by 2,173
Feynman, R. P. (1986) · Foundations of Physics · doi:10.1007/bf01886518 · Cited by 1,770
Aharonov, Y., Davidovich, L., & Zagury, N. (1993) · Physical Review A · doi:10.1103/physreva.48.1687 · Cited by 1,622
Quantum random walks: An introductory overview
Kempe, J. (2003) · Contemporary Physics · doi:10.1080/00107151031000110776 · Cited by 1,413
Two-dimensional quantum Heisenberg antiferromagnet at low temperatures
Chakravarty, S., Halperin, B. I., & Nelson, D. R. (1989) · Physical review. B, Condensed matter · doi:10.1103/physrevb.39.2344 · Cited by 1,386
Environment-assisted quantum walks in photosynthetic energy transfer
Mohseni, M., Rebentrost, P., Lloyd, S., & Aspuru-Guzik, A. (2008) · The Journal of Chemical Physics · doi:10.1063/1.3002335 · Cited by 1,189
Magnetoresistance and Hall effect in a disordered two-dimensional electron gas
Altshuler, B. L., Khmel'nitzkii, D., Larkin, A. I., & Lee, P. A. (1980) · Physical review. B, Condensed matter · doi:10.1103/physrevb.22.5142 · Cited by 1,121
Feynman, R. P. (1985) · Optics News · doi:10.1364/on.11.2.000011 · Cited by 1,023
Quantum walks: a comprehensive review
Venegas-Andraca, S. E. (2012) · Quantum Information Processing · doi:10.1007/s11128-012-0432-5 · Cited by 934
Quantum Walks of Correlated Photons
Peruzzo, A., Lobino, M., Matthews, J. C. F., Matsuda, N., Politi, A., Poulios, K., Zhou, X.-Q., Lahini, Y., Ismail, N., Wörhoff, K., et al. (2010) · Science · doi:10.1126/science.1193515 · Cited by 929
Quantum Walk in Position Space with Single Optically Trapped Atoms
Karski, M., Förster, L., Choi, J.-M., Steffen, A., Alt, W., Meschede, D., & Widera, A. (2009) · Science · doi:10.1126/science.1174436 · Cited by 659
Photons Walking the Line: A Quantum Walk with Adjustable Coin Operations
Schreiber, A., Cassemiro, K. N., Potoček, V., Gábris, A., Mosley, P. J., Andersson, E., Jex, I., & Silberhorn, C. (2010) · Physical Review Letters · doi:10.1103/physrevlett.104.050502 · Cited by 588
From quantum cellular automata to quantum lattice gases
Meyer, D. A. (1996) · Journal of Statistical Physics · doi:10.1007/bf02199356 · Cited by 556
Exploring topological phases with quantum walks
Kitagawa, T., Rudner, M. S., Berg, E., & Demler, E. (2010) · Physical Review A · doi:10.1103/physreva.82.033429 · Cited by 534
Quantum walks: a comprehensive reviewPreprint
Venegas-Andraca, S. E. (2012) · Cited by 533
Realization of a Quantum Walk with One and Two Trapped Ions
Zähringer, F., Kirchmair, G., Gerritsma, R., Solano, E., Blatt, R., & Roos, C. F. (2010) · Physical Review Letters · doi:10.1103/physrevlett.104.100503 · Cited by 531
Realization of Quantum Walks with Negligible Decoherence in Waveguide Lattices
Perets, H. B., Lahini, Y., Pozzi, F., Sorel, M., Morandotti, R., & Silberberg, Y. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.170506 · Cited by 526
From Quantum Cellular Automata To Quantum Lattice GasesPreprint
Meyer, D., Qca, F., David, Q., & Meyer, A. (1996) · Cited by 502
Anderson localization of entangled photons in an integrated quantum walk
Crespi, A., Osellame, R., Ramponi, R., Giovannetti, V., Fazio, R., Sansoni, L., De Nicola, F., Sciarrino, F., & Mataloni, P. (2013) · Nature Photonics · doi:10.1038/nphoton.2013.26 · Cited by 474
Quantum Walk of a Trapped Ion in Phase Space
Schmitz, H., Matjeschk, R., Schneider, C., Glueckert, J., Enderlein, M., Huber, T., & Schaetz, T. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.090504 · Cited by 462
Discrete Single-Photon Quantum Walks with Tunable Decoherence
Broome, M. A., Fedrizzi, A., Lanyon, B. P., Kassal, I., Aspuru-Guzik, A., & White, A. G. (2010) · Physical Review Letters · doi:10.1103/physrevlett.104.153602 · Cited by 420
Ryan, C. A., Laforest, M., Boileau, J. C., & Laflamme, R. (2005) · Physical Review A · doi:10.1103/physreva.72.062317 · Cited by 280
Self-citationBulk-boundary correspondence for chiral symmetric quantum walks
Asbóth, J. K., & Obuse, H. (2013) · Physical Review B · doi:10.1103/physrevb.88.121406 · Cited by 274
Quantum Walk on the LinePreprint
Ashwin, N., & Vishwanath, A. (2000) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0010117 · Cited by 200
Weyl, Dirac, and Maxwell equations on a lattice as unitary cellular automata
Bialynicki-Birula, I. (1994) · Physical Review D · doi:10.1103/physrevd.49.6920 · Cited by 195
Quantum walk on the line as an interference phenomenon
Knight, P. L., Roldán, E., & Sipe, J. E. (2003) · Physical Review A · doi:10.1103/physreva.68.020301 · Cited by 176
One-dimensional three-state quantum walk
Inui, N., Konno, N., & Segawa, E. (2005) · Physical Review E · doi:10.1103/physreve.72.056112 · Cited by 174
Two-particle quantum walks: Entanglement and graph isomorphism testing
Berry, S. M., & Wang, J. B. (2011) · Physical Review A · doi:10.1103/physreva.83.042317 · Cited by 156
Decoherence in the quantum walk on the line
Romanelli, A., Siri, R., Abal, G., Auyuanet, A., & Donangelo, R. (2004) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2004.08.070 · Cited by 130
Entanglement in coined quantum walks on regular graphs
Carneiro, I., Loo, M., Xu, X., Girerd, M., Kendon, V., & Knight, P. L. (2005) · New Journal of Physics · doi:10.1088/1367-2630/7/1/156 · Cited by 128
Asymptotic evolution of quantum walks with random coin
Ahlbrecht, A., Vogts, H., Werner, A. H., & Werner, R. F. (2011) · Journal of Mathematical Physics · doi:10.1063/1.3575568 · Cited by 125
Optimizing the discrete time quantum walk using a SU(2) coin
Chandrashekar, C. M., Srikanth, R., & Laflamme, R. (2008) · Physical Review A · doi:10.1103/physreva.77.032326 · Cited by 121
Self-citationQuantum walks on a random environment
Yin, Y., Katsanos, D. E., & Evangelou, S. N. (2008) · Physical Review A · doi:10.1103/physreva.77.022302 · Cited by 120
Localization and fractality in inhomogeneous quantum walks with self-duality
Shikano, Y., & Katsura, H. (2010) · Physical Review E · doi:10.1103/physreve.82.031122 · Cited by 117
Strauch, F. W. (2006) · Physical Review A · doi:10.1103/physreva.73.054302 · Cited by 115
Dynamical Localization of Quantum Walks in Random Environments
Joye, A., & Merkli, M. (2010) · Journal of Statistical Physics · doi:10.1007/s10955-010-0047-0 · Cited by 113
Discrete Single-Photon Quantum Walks With Tunable Decoherence
Broome, M. A., Fedrizzi, A., Lanyon, B. P., Kassal, I., Aspuru‐Guzik, A., & White, A. G. (2010) · Frontiers in Optics · doi:10.1364/fio.2010.pdpb1 · Cited by 110
Relationship between quantum walks and relativistic quantum mechanics
Chandrashekar, C. M., Banerjee, S., & Srikanth, R. (2010) · Physical Review A · doi:10.1103/physreva.81.062340 · Cited by 109
Self-citationDerivation of the Dirac equation from principles of information processing
D'Ariano, G. M., & Perinotti, P. (2014) · Physical Review A · doi:10.1103/physreva.90.062106 · Cited by 103
Quantum walk on the line: Entanglement and nonlocal initial conditions
Abal, G., Siri, R., Romanelli, A., & Donangelo, R. (2006) · Physical Review A · doi:10.1103/physreva.73.042302 · Cited by 101
Breakdown of an Electric-Field Driven System: A Mapping to a Quantum Walk
Oka, T., Konno, N., Arita, R., & Aoki, H. (2005) · Physical Review Letters · doi:10.1103/physrevlett.94.100602 · Cited by 101
Localization of an inhomogeneous discrete-time quantum walk on the line
Konno, N. (2009) · Quantum Information Processing · doi:10.1007/s11128-009-0147-4 · Cited by 99
Dynamically Disordered Quantum Walk as a Maximal Entanglement Generator
Vieira, R., Amorim, E. P. M., & Rigolin, G. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.180503 · Cited by 79
Chandrashekar, C. M. (2013) · Scientific Reports · doi:10.1038/srep02829 · Cited by 64
Self-citationDynamical localization for d-dimensional random quantum walks
Joye, A. (2012) · Quantum Information Processing · doi:10.1007/s11128-012-0406-7 · Cited by 61
Disordered-quantum-walk-induced localization of a Bose-Einstein condensate
Chandrashekar, C. M. (2011) · Physical Review A · doi:10.1103/physreva.83.022320 · Cited by 58
Self-citationAnderson localization in generalized discrete-time quantum walks
Vakulchyk, I., Fistul, M. V., Qin, P., & Flach, S. (2017) · Physical review. B./Physical review. B · doi:10.1103/physrevb.96.144204 · Cited by 58
Godoy, S., & Fujita, S. (1992) · The Journal of Chemical Physics · doi:10.1063/1.463812 · Cited by 47
Dirac Cellular Automaton from Split-step Quantum Walk
Mallick, A., & Chandrashekar, C. M. (2016) · Scientific Reports · doi:10.1038/srep25779 · Cited by 45
Self-citationRao, B. R., Srikanth, R., Chandrashekar, C. M., & Banerjee, S. (2011) · Physical Review A · doi:10.1103/physreva.83.064302 · Cited by 44
Self-citationAnderson localization of a one-dimensional quantum walker
Derevyanko, S. (2018) · Scientific Reports · doi:10.1038/s41598-017-18498-1 · Cited by 40
Generalized quantum walk in momentum space
Romanelli, A., Auyuanet, A., Siri, R., Abal, G., & Donangelo, R. (2005) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2005.01.026 · Cited by 36
Chandrashekar, C. M. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1212.5984 · Cited by 35
Self-citationQuantum correlations in continuous-time quantum walks of two indistinguishable particles
Benedetti, C., Buscemi, F., & Bordone, P. (2012) · Physical Review A · doi:10.1103/physreva.85.042314 · Cited by 30
Kudo, K., & Deguchi, T. (2018) · Physical review. B./Physical review. B · doi:10.1103/physrevb.97.220201 · Cited by 26
Kumar, N. P., Balu, R., Laflamme, R., & Chandrashekar, C. M. (2018) · Physical Review A · doi:10.1103/physreva.97.012116 · Cited by 24
Self-citationAsymptotic properties of the Dirac quantum cellular automaton
Pérez, A. (2016) · Physical Review A · doi:10.1103/physreva.93.012328 · Cited by 18
Quantum walk on distinguishable non-interacting many-particles and indistinguishable two-particle
Chandrashekar, C. M., & Busch, T. (2012) · Quantum Information Processing · doi:10.1007/s11128-012-0387-6 · Cited by 16
Self-citationAbal, G., Siri, R., Romanelli, A., & Donangelo, R. (2006) · Physical Review A · doi:10.1103/physreva.73.069905 · Cited by 15
Chandrashekar, C. M., Srikanth, R., & Laflamme, R. (2010) · Physical Review A · doi:10.1103/physreva.82.019902 · Cited by 14
Self-citationEntanglement Properties of Localized States in 1D Topological Quantum WalksPreprint
Chandrashekar, C. M., Obuse, H., & Busch, T. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1502.00436 · Cited by 13
Self-citationEntanglement Generation in Spatially Separated Systems Using Quantum Walk
Chandrashekar, C. M., Goyal, S. K., & Banerjee, S. (2012) · Journal of Quantum Information Science · doi:10.4236/jqis.2012.22004 · Cited by 11
Self-citationInterference and correlated coherence in disordered and localized quantum walkPreprint
Singh, S., & Chandrashekar, C. M. (2017) · arXiv (Cornell University) · Cited by 4
Self-citation
Flagged first, then by citations
1 of the 70 references couldn’t be matched to a known paper.
Research works printed but not linked: 2
- Riazanov, 1958, The Feynman path integral for the Dirae equation, Zh. Eksp. Teor. Fiz., 33, 1437
- Riazanov, 1958, Sov. Phys. JETP, 6, 1107
Cited by
Sorted by citations
Quantum walks and Dirac cellular automata on a programmable trapped-ion quantum computer
Huerta Alderete, C., Singh, S., Nguyen, N. H., Zhu, D., Balu, R., Monroe, C., Chandrashekar, C. M., & Linke, N. M. (2020) · Nature Communications · doi:10.1038/s41467-020-17519-4 · Cited by 48
Self-citationMulti-bit quantum random number generation from a single qubit quantum walk
Sarkar, A., & Chandrashekar, C. M. (2019) · Scientific Reports · doi:10.1038/s41598-019-48844-4 · Cited by 26
Self-citationPires, M. A., Molfetta, G. D., & Queirós, S. M. D. (2019) · Scientific Reports · doi:10.1038/s41598-019-55642-5 · Cited by 25
Revisiting one-dimensional discrete-time quantum walks with general coin
Jayakody, M. N., Meena, C., & Pradhan, P. (2023) · Physics Open · doi:10.1016/j.physo.2023.100189 · Cited by 14
Fang, X., An, K., Zhang, B., Sanders, B. C., & Lu, H. (2023) · Physical Review A · doi:10.1103/physreva.107.012433 · Cited by 14
Negative correlations can play a positive role in disordered quantum walks
Pires, M. A., & Queirós, S. M. D. (2021) · Scientific Reports · doi:10.1038/s41598-021-84073-4 · Cited by 13
Naves, C. B., Pires, M. A., Soares-Pinto, D. O., & Queirós, S. M. D. (2022) · Physical Review A · doi:10.1103/physreva.106.042408 · Cited by 12
One-dimensional quantum walks driven by two-entangled-qubit coins
Panahiyan, S., & Fritzsche, S. (2020) · Physics Letters A · doi:10.1016/j.physleta.2020.126673 · Cited by 7
A systematic method to building Dirac quantum walks coupled to electromagnetic fields
Jay, G., Debbasch, F., & Wang, J. B. (2020) · Quantum Information Processing · doi:10.1007/s11128-020-02933-w · Cited by 6
Naves, C. B., Pires, M. A., Soares-Pinto, D. O., & Queirós, S. M. D. (2023) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/acbd25 · Cited by 5
Gravitationally induced entanglement dynamics between two quantum walkers
Badhani, H., & Chandrashekar, C. M. (2021) · The European Physical Journal C · doi:10.1140/epjc/s10052-021-09243-0 · Cited by 5
Self-citationCharacterization of anomalous diffusion in one-dimensional quantum walks
Hegde, A. S., & Chandrashekar, C. M. (2022) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ac6b67
Self-citationSpatial entanglement between two quantum walkers with exchange symmetric coins
Muhammad, I. Y., Deesuwan, T., Yoo-Kong, S., Tangwancharoen, S., & Танаситтикосол, М. (2024) · Physics Letters A · doi:10.1016/j.physleta.2024.129758
Ximenes, J. J., Pires, M. A., & Villas-Bôas, J. M. (2026) · Physical Review A · doi:10.1103/h26t-g6c7
Metadata
- Authors
- Singh, S., Balu, R., Laflamme, R., & Chandrashekar, C. M.
- Affiliations
- Homi Bhabha National Institute (IN)
- DEVCOM Army Research Laboratory (US)
- University of Waterloo (CA)
- Venue
- Journal of Physics Communications
- Publisher
- IOP Publishing
- Published
- 2019-05-01
- Volume
- 3
- Issue
- 5
- Pages
- 055008
- ISSN
- 2399-6528 (ISSN-L)
- OpenAlex
- W2953359391
- Cited by
- 14
- References
- 70
- Citations by year
- 2026: 1 · 2024: 1 · 2023: 3 · 2022: 2 · 2021: 2 · 2020: 3 · 2019: 2
- FWCI
- 0.91
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- Journal of Physics Communications (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Science and Engineering Research Board (SB/SN/RJN-192/2014)
- Department of Science and Technology, Government of India (DST/ICPS/QuST/Theme-1/2019.)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Keywords
- discrete-time quantum walks, two-particle entanglement, entanglement generation, localization, delocalization, phase disorder, Dirac equation, accelerated particles, relativistic quantum mechanics, quantum simulation
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-11-10, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-11-10 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
