The DOI matches its Crossref record; 21 of the 22 references it cites were found in a registry or an index; none of the 9 sources its claims cite is checked for support yet.
Entanglement and Non-Markovianity of Quantum Evolutions
Open accessAbstract
We address the problem of quantifying the non-markovian character of quantum time evolutions of general systems in contact with an environment. We introduce two different measures of non-markovianity that exploit the specific traits of quantum correlations and are suitable for opposite experimental contexts. When complete tomographic knowledge about the evolution is available, our measure provides a necessary and sufficient condition to quantify strictly the non-markovianity. In the opposite case, when no information whatsoever is available, we propose a sufficient condition for non-markovianity. Remarkably, no optimization procedure underlies our derivation, which greatly enhances the practical relevance of the proposed criteria.
Overview
AI snapshot
Written from the paper’s full text.
TL;DR
The paper introduces two measures of non-Markovianity for quantum evolutions that avoid optimization: an entanglement-based sufficient condition usable when the dynamics is unknown, and a necessary-and-sufficient CP-divisibility measure when the dynamical map can be reconstructed. It illustrates the approach with a damped harmonic oscillator coupled to Ohmic and super-Ohmic baths and with a qubit pure-dephasing model.
Key findings
- A sufficient condition for non-Markovianity is \(I(\mathcal{E})>0\), obtained by preparing a maximally entangled system-ancilla state and checking for non-monotonic decay of entanglement; Markovian evolutions give \(I(\mathcal{E})=0\).
- When the dynamical map is known, non-Markovianity is equivalent to the existence of times \(t,\epsilon\) such that \(\mathcal{E}(t+\epsilon,t)\) is not completely positive; the proposed measure uses \(f_{\mathrm{NCP}}\), \(g(t)\ge 0\), and \(I=\int g(t)\,dt\), with normalized \(D_{\mathrm{NM}}=I/(I+1)\) so that \(D_{\mathrm{NM}}=0\) for Markovian and \(D_{\mathrm{NM}}\to 1\) for \(I\to\infty\).
- For a damped harmonic oscillator with Ohmic bath \(J(\omega)=\alpha\omega e^{-\omega/\omega_c}\), the simulations show that \(\alpha\to 0\) approaches Markovian evolution independently of temperature \(T\), while the onset of non-Markovianity is \(T\)-dependent: the coupling \(\alpha\) at which \(I(\mathcal{E})\) becomes nonzero increases with increasing temperature, as does \(I(\mathcal{E})\) for sufficiently large \(\alpha\).
- A super-Ohmic bath \(J(\omega)=\alpha\omega^3 e^{-\omega/\omega_c}\) shows analogous behavior, but the specific value of \(I(\mathcal{E})\) for given \(T\) and \(\alpha\) depends strongly on the bath spectral function; for qubit pure dephasing \(d\rho/dt=\gamma(t)(\sigma_z\rho\sigma_z-\rho)\), \(I\) is proportional to the area of \(\gamma(t)\) below zero, and if negative \(\gamma(t)\) does not tend to zero fast enough then \(I\to\infty\), as with \(\gamma(t)\sim\tan(t)\).
Methods
- Theoretical proposal with two criteria: an entanglement-based sufficient condition for unknown dynamics, and a necessary-and-sufficient condition based on complete positivity of infinitesimal dynamical maps when the evolution can be exactly reconstructed, e.g. by process tomography or a microscopic model.
- For the unknown-dynamics measure, a maximally entangled state \(|\Phi\rangle=\frac{1}{\sqrt{d}}\sum_{n=0}^{d-1}|n\rangle|n\rangle\) is prepared between the system and an isolated ancilla, and the entanglement is monitored over \([t_0,t_{\max}]\).
- Illustrative simulations use a single damped harmonic oscillator coupled to a bath under the rotating wave approximation, with Ohmic and super-Ohmic spectral densities, several temperatures, and varying coupling strengths; entanglement is quantified by logarithmic negativity for Gaussian states.
Limitations
- The paper states that the entanglement-based criterion is only sufficient: there can be non-Markovian quantum evolutions that remain undetected because \(I(\mathcal{E})>0\) is not necessary.
- The necessary-and-sufficient measure requires exact reconstruction of the dynamical map; if \(\mathcal{E}(t,0)\) is not invertible for larger times, \(\mathcal{E}(t+\epsilon,t)\) cannot be defined unequivocally, and the integral measure is finite only if \(g(t)\) decreases fast enough, which “will not be always the case.”
- The simulations use a discrete and finite number of bath oscillators, which the authors say affects the results; they choose parameters so that \(t_{\max}\) is shorter than the bath recurrence time. Evident from the text: the work is theoretical/simulated and does not report experimental validation.
Model-written summary. Check it against the paper before relying on it.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
0 of 9 cited sources checked · 0 supported · 0 flagged
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“the same happens with the value of I ( E ) itself for α large enough.”
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passes- The authors state this as an assumption: The rotating wave approximation (RWA) is valid in the model.
- The authors state this as an assumption: The bath is initially in a thermal state.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“It is clear from Fig. 2 that in the limit α → 0 we approach a Markovian evolution independently of the value of T .”
Load-bearingStrength:boosted· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: The rotating wave approximation (RWA) is valid in the model.
- The authors state this as an assumption: The bath is initially in a thermal state.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“An analogous situation is encountered in the presence of a super-Ohmic spectral density J ( ω ) = αω 3 e -ω/ω c , as shown in figure 3; however, the specific value of I ( E ) for given T and α depends strongly on the bath spectral function.”
Strength:boosted· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passes- The authors state this as an assumption: The rotating wave approximation (RWA) is valid in the model.
- The authors state this as an assumption: The bath is initially in a thermal state.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“whereas the on-set of deviations from Markovianity for stronger coupling strengths are T -dependent, so that the value of α for which the measure I ( E ) becomes nonzero increases with increasing temperature”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: The rotating wave approximation (RWA) is valid in the model.
- The authors state this as an assumption: The bath is initially in a thermal state.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Therefore, for this kind of evolution, I is proportional to the area of γ ( t ) which is below zero.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“then it is possible to prove that if and only if L t can be written in the standard form (1), with H ( t ), γ k ( t ) ≥ 0 and V k ( t ) potentially time dependent, the family of propagators E ( t 2 ,t 1 ) = T exp ( ∫ t 2 t 1 L τ dτ ) satisfying the composition law”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“in such a way that if the evolution of the system is Markovian the derivative of E [ ρ SA ( t )] is always negative and I ( E ) = 0.”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesNone of the sources cited for this claim have been checked yet.
In the paper
“The actual dynamics of any real open quantum system is expected to deviate to some extent from the idealized Markovian evolution that arises from the conditions of weak (or singular) coupling to a memoryless reservoir [1, 2].”
Load-bearingStrength:hedged· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“There can be however non-Markovian quantum evolutions that remain undetected by the proposed measure”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“However if and only if there exist times t and ǫ such that E ( t + ǫ,t ) is not CP, the dynamics will be non-Markovian.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
- Probably not a substantial claim. 6
- The quote only partly states this claim. 1
- It may state two separate claims as one. 6
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“although the shape of the curves does not depend significatively on r .”
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
- The authors state this as an assumption: The rotating wave approximation (RWA) is valid in the model.
- The authors state this as an assumption: The bath is initially in a thermal state.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“the other provides a measure which quantify strictly the non-Markovianity, provided that the structural form of the dynamical map is known.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe quote only partly states this claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“noticing that g ( t ) ≥ 0, with g ( t ) = 0 if and only if E ( t + ǫ,t ) is CP.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Therefore, E ( t + ǫ,t ) is CP if and only if f NCP ( t + ǫ, t ) = 1, otherwise f NCP ( t + ǫ, t ) > 1.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Note that since the knowledge of the exact form of the dynamics is not necessary to measure I ( E ) , this method can be particularly useful in the study of infinite dimensional systems, where the computation of the exact dynamical map is often difficult.”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
In the paper
“However, if the evolution is non-Markovian, the requirement of strict monotonicity does no longer hold [11], as environmental correlations can lead to bipartite entanglement to be increased and decreased as a function of time”
What the sources say
- Not checked yetcites [11] source
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
In the paper
“The structure of this kind of semigroups was analyzed in detail some time ago [8], concluding that a quantum system will undergo a Markovian dynamics provided that its evolution satisfies a Master equation of the standard”
What the sources say
- Not checked yetcites [8] source
Strength:boosted· not yet calibratedCausal:conditional· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“can be taken as a measure of non-Markovianity, and as long as g ( t ) decreases fast enough (this will not be always the case) will be finite.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim. It may state two separate claims as one.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“In the simulation, of course, the discrete and finite number of oscillators in the bath will affect the results, but in order to avoid this effect we have taken a number of oscillators distributed in a range of frequencies (see details on the plots) such that our final time t max is shorter than the recurrence time of the bath but large enough to capture the general properties of the dynamics.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim. It may state two separate claims as one.
- The authors state this as an assumption: The rotating wave approximation (RWA) is valid in the model.
- The authors state this as an assumption: The bath is initially in a thermal state.
In the paper
“This is particularly the case when considering interacting many-body systems, where the subsystem's coupling strength may be comparable to the coupling to the bath [4].”
What the sources say
- Not checked yetcites [4] source
Strength:hedged· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
The paper relies on this without support.
An accurate microscopic model of the system-bath interaction may be unfeasible, especially for many-body systems.
“The exact details of what makes a given quantum evolution non-Markovian may be complicated, and in many cases, especially when thinking about many-body systems, an accurate microscopic model of the system-bath interaction may actually be unfeasible.”
The authors state this as an assumption.
The rotating wave approximation (RWA) is valid in the model.
“we have assumed the validity of the rotating wave approximation (RWA).”
The authors state this as an assumption.
The bath is initially in a thermal state.
“The bath is assumed to be initially in a thermal state ρ B = exp( -H B /T ) / tr [exp ( -H B /T )]”
The paper relies on this without support.
The ancillary system remains isolated from decoherence sources.
“an ancillary system which has to remain isolated from the decoherence sources”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The cited source says what the claim attributes to it.
In the citing paper
“The above equation describes Markovian dynamics for Γ k ≥ 0 . Whenever the loss rate Γ k becomes negative (Fleming and Hu, 2012; Rivas et al. , 2010), Eq. (52) can also describe non-Markovian dynamics (Bastidas et al. , 2018; Kyaw et al. , 2020a; Tan et al. , 2010).”
From Noisy intermediate-scale quantum algorithms (2022) · cites this paper as Rivas et al., 2010
In the citing paper
“Our results are applicable to a wide variety of scenarios including bounding decoherence rates [40], and quantum speed limits in dissipative state preparation [41], quantum computation and simulation assisted by dissipation [42].”
From Quantum Speed Limits in Open System Dynamics (2013) · cites this paper as [40]
In the citing paper
“This measure provides a necessary and sufficient condition for a given evolution to depart from strict Markovianity by means of evaluating whether or not the associated dynamical map E ( t + ǫ,t ) is completely positive (CP) for any ǫ .”
From Non-Markovianity-Assisted Steady State Entanglement (2012) · cites this paper as [19]
In the citing paper
“The two measures that we will consider here [12, 13] actually respectively rely on the violation of the quantum analog of the classical properties of P-divisibility and monotonic decrease in time of the Kolmogorov distance, that we have considered in Sect. III and hold true for the Markovian case, while also other approaches have been considered [11].”
From Markovianity and non-Markovianity in quantum and classical systems (2011) · cites this paper as [13]
In the citing paper
“These two criteria are at the basis of two recently introduced measures of non-Markovianity for open quantum systems [12, 13], which we here compare considering a quantum counterpart of classical semiMarkov processes.”
From Markovianity and non-Markovianity in quantum and classical systems (2011) · cites this paper as [13]
In the citing paper
“In particular, as shown by Eq. (64) and Eq. (67) and discussed thoroughly in Sect. IV B 3, we put into evidence that the measure based on CP-divisibility [13] gives the same infinite value to quite different time evolutions, at variance with the measure based on the dynamics of the trace distance [12], which assigns to them different weights.”
From Markovianity and non-Markovianity in quantum and classical systems (2011) · cites this paper as [13]
In the citing paper
“Recent work has demonstrated that the retention of quantum dynamics in biological systems is intricately connected with environmental fluctuations taking place at biologically relevant length and time scales [51–55].”
From The origins of quantum biology (2018) · cites this paper as [53]
In the citing paper
“Note that the shift is independent of the temperature, and although its effect is typically small (e.g.[3,18]), we will not neglect it in our study.”
From Markovian master equations: a critical study (2010) · cites this paper as [18]
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.
Unknown-dynamics criterion is called both necessary and sufficient
MinorThe paper says this criterion can miss some non-Markovian evolutions, and later explicitly calls a positive result sufficient for non-Markovianity. Calling it a necessary condition for detecting deviations contradicts those statements.
“This will allow us to give a necessary condition to measure deviations from Markovianity even when the actual form of the dynamics is completely unknown, although some non-Markovian evolutions may be undetected.”
“There can be however non-Markovian quantum evolutions that remain undetected by the proposed measure, given that the requirement I ( E ) > 0 is a sufficient condition for deviation from Markovianity.”
Entanglement derivative need not be strictly negative for Markovian evolution
MinorThe identity evolution is Markovian but leaves entanglement constant, giving a zero derivative rather than an always-negative one.
“if the evolution of the system is Markovian the derivative of E [ ρ SA ( t )] is always negative and I ( E ) = 0.”
“1 is trivially Markovian”
Citations
Cites
On the generators of quantum dynamical semigroups
Lindblad, G. (1976) · Communications in Mathematical Physics · doi:10.1007/bf01608499 · Cited by 7,548
The Theory of Open Quantum Systems
Breuer, H.-P., & Petruccione, F. (2007) · doi:10.1093/acprof:oso/9780199213900.001.0001 · Cited by 5,938
Markov Processes: Characterization and Convergence.
Abakuks, A., Ethier, S. N., & Kurtz, T. G. (1987) · Biometrics · doi:10.2307/2531839 · Cited by 4,471
Completely positive dynamical semigroups of N -level systems
Gorini, V., Kossakowski, A., & Sudarshan, E. C. G. (1976) · Journal of Mathematical Physics · doi:10.1063/1.522979 · Cited by 3,998
Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems
Engel, G. S., Calhoun, T. R., Read, E. L., Ahn, T.-K., Mančal, T., Cheng, Y.-C., Blankenship, R. E., & Fleming, G. R. (2007) · Nature · doi:10.1038/nature05678 · Cited by 3,315
Completely positive linear maps on complex matrices
Choi, M.-D. (1975) · Linear Algebra and its Applications · doi:10.1016/0024-3795(75)90075-0 · Cited by 2,659
Logarithmic Negativity: A Full Entanglement Monotone That is not Convex
Plenio, M. B. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.090503 · Cited by 1,530
Self-citationLinear transformations which preserve trace and positive semidefiniteness of operators
Jamiołkowski, A. (1972) · Reports on Mathematical Physics · doi:10.1016/0034-4877(72)90011-0 · Cited by 1,512
Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems
Breuer, H.-P., Laine, E.-M., & Piilo, J. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.210401 · Cited by 1,480
Effective Quantum Spin Systems with Trapped Ions
Porras, D., & Cirac, J. I. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.207901 · Cited by 872
Flagged first, then by citations
1 of the 22 references couldn’t be matched to a known paper.
Research works printed but not linked: 2
- A. Kossakowski, 1972, Bull. Acad. Polon. Sci., Sér. Sci. Math., 20, 1021
- M. Reed, 1975, Methods of Modern Mathematical Physics II
Cited by
Sorted by citations
Items 201–300 of 1,000
Generalized Pauli channels and a class of non-Markovian quantum evolution
Chruściński, D., & Siudzińska, K. (2016) · Physical Review A · doi:10.1103/physreva.94.022118 · Cited by 44
Efficient real-time path integrals for non-Markovian spin-boson models
Strathearn, A., Lovett, B. W., & Kirton, P. (2017) · New Journal of Physics · doi:10.1088/1367-2630/aa8744 · Cited by 48
Entanglement evolution of two qubits under noisy environments
Li, J., Zou, J., & Shao, B. (2010) · Physical Review A · doi:10.1103/physreva.82.042318 · Cited by 43
Phase Covariant Qubit Dynamics and Divisibility
Filippov, S. N., Glinov, A. N., & Leppäjärvi, L. (2020) · Lobachevskii Journal of Mathematics · doi:10.1134/s1995080220040095 · Cited by 43
Non-Markovian decoherence dynamics in nonequilibrium environments
Cai, X.-J., & Zheng, Y. (2018) · The Journal of Chemical Physics · doi:10.1063/1.5039891 · Cited by 43
Quantum Simulation of Dissipative Processes without Reservoir Engineering
Candia, R. D., Pedernales, J. S., del Campo, A., Solano, E., & Casanova, J. (2015) · Scientific Reports · doi:10.1038/srep09981 · Cited by 44
Non-Markovian dynamics of quantum coherence of two-level system driven by classical field
Huang, Z., & Situ, H. (2017) · Quantum Information Processing · doi:10.1007/s11128-017-1673-0 · Cited by 42
Facets of quantum information under non-Markovian evolution
Naikoo, J., Dutta, S., & Banerjee, S. (2019) · Physical Review A · doi:10.1103/physreva.99.042128 · Cited by 42
Global correlation and local information flows in controllable non-Markovian open quantum dynamics
Chen, X., Zhang, N., He, W., Kong, X., Tao, M., Deng, F., Ai, Q., & Long, G. (2022) · npj Quantum Information · doi:10.1038/s41534-022-00537-z · Cited by 43
Preservation Macroscopic Entanglement of Optomechanical Systems in non-Markovian Environment
Cheng, J., Zhang, W.-Z., Zhou, L., & Zhang, W. (2016) · Scientific Reports · doi:10.1038/srep23678 · Cited by 42
System–environment correlations and non-Markovian dynamics
Pernice, A., Helm, J., & Strunz, W. T. (2012) · Journal of Physics B Atomic Molecular and Optical Physics · doi:10.1088/0953-4075/45/15/154005 · Cited by 41
Role of environmental correlations in the non-Markovian dynamics of a spin system
Lorenzo, S., Plastina, F., & Paternostro, M. (2011) · Physical Review A · doi:10.1103/physreva.84.032124 · Cited by 43
Optical Feedback-Enhanced Photon Entanglement from a Biexciton Cascade
Hein, S. M., Schulze, F., Carmele, A., & Knorr, A. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.027401 · Cited by 41
Objectivity in the non-Markovian spin-boson model
Lampo, A., Tuziemski, J., Lewenstein, M., & Korbicz, J. K. (2017) · Physical Review A · doi:10.1103/physreva.96.012120 · Cited by 44
Non-Markovian continuous-time quantum walks on lattices with dynamical noise
Benedetti, C., Buscemi, F., Bordone, P., & Paris, M. G. A. (2016) · Physical Review A · doi:10.1103/physreva.93.042313 · Cited by 41
Non-Markovian dynamics of a two-level system in the presence of hierarchical environments
Man, Z., An, N. B., & Xia, Y. (2015) · Optics Express · doi:10.1364/oe.23.005763 · Cited by 40
Entanglement control via reservoir engineering in ultracold atomic gases
McEndoo, S., Haikka, P., Chiara, G. D., Palma, G. M., & Maniscalco, S. (2013) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/101/60005 · Cited by 40
Reconstructing non-Markovian quantum dynamics with limited control
Milz, S., Pollock, F. A., & Modi, K. K. (2018) · Physical Review A · doi:10.1103/physreva.98.012108 · Cited by 40
Witnessing non-Markovian effects of quantum processes through Hilbert-Schmidt speed
Jahromi, H. R., Mahdavipour, K., Shadfar, M. K., & Franco, R. L. (2020) · Physical Review A · doi:10.1103/physreva.102.022221 · Cited by 40
An Invitation to Quantum Channels
Jagadish, V., & Petruccione, F. (2018) · Quanta · doi:10.12743/quanta.v7i1.77 · Cited by 39
Dynamical quantum phase transitions and non-Markovian dynamics
Kyaw, T. H., Bastidas, V. M., Tangpanitanon, J., Romero, G., & Kwek, L. C. (2020) · Physical Review A · doi:10.1103/physreva.101.012111 · Cited by 39
Role of information backflow in the emergence of quantum Darwinism
Milazzo, N., Lorenzo, S., Paternostro, M., & Palma, G. M. (2019) · Physical Review A · doi:10.1103/physreva.100.012101 · Cited by 39
Synchronization and non-Markovianity in open quantum systems
Karpat, G., Yalçınkaya, İ., Çakmak, B., Giorgi, G. L., & Zambrini, R. (2021) · Physical Review A · doi:10.1103/physreva.103.062217 · Cited by 43
Accuracy of the Quantum Regression Theorem for Photon Emission from a Quantum Dot
Cosacchi, M., Seidelmann, T., Cygorek, M., Vagov, A., Reiter, D. E., & Axt, V. M. (2021) · Physical Review Letters · doi:10.1103/physrevlett.127.100402 · Cited by 41
Effects of the rotating-wave and secular approximations on non-Markovianity
Mäkelä, H., & Möttönen, M. (2013) · Physical Review A · doi:10.1103/physreva.88.052111 · Cited by 43
Non-Markovian quantum exceptional points
Lin, J.-D., Kuo, P.-C., Lambert, N., Miranowicz, A., Nori, F., & Chen, Y.-N. (2025) · Nature Communications · doi:10.1038/s41467-025-56242-w · Cited by 38
Rossi, M. A. C., & Paris, M. G. A. (2016) · The Journal of Chemical Physics · doi:10.1063/1.4939733 · Cited by 38
Revealing memory effects in phase-covariant quantum master equations
Teittinen, J., Lyyra, H., Sokolov, B., & Maniscalco, S. (2018) · New Journal of Physics · doi:10.1088/1367-2630/aacc38 · Cited by 39
Non-Markovianity of Gaussian Channels
Torre, G., Roga, W., & Illuminati, F. (2015) · Physical Review Letters · doi:10.1103/physrevlett.115.070401 · Cited by 40
Unification of witnessing initial system-environment correlations and witnessing non-Markovianity
Rodríguez-Rosario, C. A., Modi, K. K., Mazzola, L., & Aspuru‐Guzik, A. (2012) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/99/20010 · Cited by 38
Quantum non-Markovianity: Overview and recent developments
Utagi, S., & Mandayam, P. (2023) · Frontiers in Quantum Science and Technology · doi:10.3389/frqst.2023.1134583 · Cited by 49
Quantum discord and non-Markovianity of quantum dynamics
Alipour, S., Mani, A., & Rezakhani, A. T. (2012) · Physical Review A · doi:10.1103/physreva.85.052108 · Cited by 37
Efficiency of quantum controlled non-Markovian thermalization
Mukherjee, V., Giovannetti, V., Fazio, R., Huelga, S. F., Calarco, T., & Montangero, S. (2015) · New Journal of Physics · doi:10.1088/1367-2630/17/6/063031 · Cited by 39
Self-citationNon-Markovian effects in electronic and spin transport
Ribeiro, P., & Vieira, V. R. (2015) · Physical Review B · doi:10.1103/physrevb.92.100302 · Cited by 37
Decoherence induced by non-Markovian noise in a nonequilibrium environment
Cai, X.-J., & Zheng, Y. (2016) · Physical Review A · doi:10.1103/physreva.94.042110 · Cited by 37
Brito, F., & Werlang, T. (2015) · New Journal of Physics · doi:10.1088/1367-2630/17/7/072001 · Cited by 36
Controlling entropic uncertainty bound through memory effects
Karpat, G., Piilo, J., & Maniscalco, S. (2015) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/111/50006 · Cited by 36
Operational Characterization of Divisibility of Dynamical Maps
Bae, J., & Chruściński, D. (2016) · Physical Review Letters · doi:10.1103/physrevlett.117.050403 · Cited by 36
Non-Markovian effect on quantum Otto engine: Role of system-reservoir interaction
Shirai, Y., Hashimoto, K., Tezuka, R., Uchiyama, C., & Hatano, N. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.023078 · Cited by 37
Entropic Bounds on Information Backflow
Megier, N., Smirne, A., & Vacchini, B. (2021) · Physical Review Letters · doi:10.1103/physrevlett.127.030401 · Cited by 36
Dynamics and thermodynamics of a central spin immersed in a spin bath
Mukhopadhyay, C., Bhattacharya, S., Misra, A., & Pati, A. K. (2017) · Physical Review A · doi:10.1103/physreva.96.052125 · Cited by 37
Programmable entanglement oscillations in a non-Markovian channel
Cialdi, S., Brivio, D., Tesio, E., & Paris, M. G. A. (2011) · Physical Review A · doi:10.1103/physreva.83.042308 · Cited by 35
Gaikwad, C., Kowsari, D., Brame, C., Song, X., Zhang, H., Esposito, M., Ranadive, A., Cappelli, G., Roch, N., Levenson-Falk, E. M., et al. (2024) · Physical Review Letters · doi:10.1103/physrevlett.132.200401 · Cited by 38
Feshbach Projection Formalism for Open Quantum Systems
Chruściński, D., & Kossakowski, A. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.050402 · Cited by 35
Exact non-Markovian master equation for the spin-boson and Jaynes-Cummings models
Ferialdi, L. (2017) · Physical Review A · doi:10.1103/physreva.95.020101 · Cited by 35
Quantum spin chain dissipative mean-field dynamics
Benatti, F., Carollo, F., Roberto Floreanini, B., & Narnhofer, H. (2018) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/aacbdb · Cited by 35
Exact master equation and general non-Markovian dynamics in open quantum systems
Zhang, W.-M. (2019) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2018-800047-4 · Cited by 35
Information flow versus divisibility for qubit evolution
Chakraborty, S., & Chruściński, D. (2019) · Physical Review A · doi:10.1103/physreva.99.042105 · Cited by 36
Convex resource theory of non-Markovianity
Bhattacharya, S., Bhattacharya, B., & Majumdar, A. S. (2020) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/abd191 · Cited by 35
Capturing non-Markovian dynamics with the reaction coordinate method
Anto-Sztrikacs, N., & Segal, D. (2021) · Physical Review A · doi:10.1103/physreva.104.052617 · Cited by 35
Khurana, D., Agarwalla, B. K., & Mahesh, T. S. (2019) · Physical Review A · doi:10.1103/physreva.99.022107 · Cited by 37
Non-Markovianity and memory effects in quantum open systems
Hou, S. C., Liang, S.-N., & Yi, X. X. (2015) · Physical Review A · doi:10.1103/physreva.91.012109 · Cited by 35
Admissible memory kernels for random unitary qubit evolution
Wudarski, F., Należyty, P., Sarbicki, G., & Chruściński, D. (2015) · Physical Review A · doi:10.1103/physreva.91.042105 · Cited by 34
General structure of quantum collisional models
Vacchini, B. (2014) · International Journal of Quantum Information · doi:10.1142/s0219749914610115 · Cited by 34
Trapani, J., Bina, M., Maniscalco, S., & Paris, M. G. A. (2015) · Physical Review A · doi:10.1103/physreva.91.022113 · Cited by 34
Coarse graining a non-Markovian collisional model
Bernardes, N. K., Carvalho, A. R. R., Monken, C. H., & Santos, M. F. (2017) · Physical Review A · doi:10.1103/physreva.95.032117 · Cited by 35
Conditional past-future correlation induced by non-Markovian dephasing reservoirs
Budini, A. A. (2019) · Physical Review A · doi:10.1103/physreva.99.052125 · Cited by 34
Non-Markovian fermionic stochastic Schrödinger equation for open system dynamics
Shi, W., Zhao, X., & Yu, T. (2013) · Physical Review A · doi:10.1103/physreva.87.052127 · Cited by 34
Non-Markovianity in atom-surface dispersion forces
Intravaia, F., Behunin, R. O., Henkel, C., Busch, K., & Dalvit, D. A. R. (2016) · Physical Review A · doi:10.1103/physreva.94.042114 · Cited by 34
Quantum Speed Limit of a Photon under Non-Markovian Dynamics
Xu, Z.-Y., & Zhu, S.-Q. (2014) · Chinese Physics Letters · doi:10.1088/0256-307x/31/2/020301 · Cited by 33
Measurement of quantum memory effects and its fundamental limitations
Wittemer, M., Clos, G., Breuer, H., Warring, U., & Schaetz, T. (2018) · Physical Review A · doi:10.1103/physreva.97.020102 · Cited by 34
Hierarchical-environment-assisted non-Markovian speedup dynamics control
Xu, K. D., Zhang, Y.-J., Xia, Y., Wang, Z.-K., & Fan, H. (2018) · Physical Review A · doi:10.1103/physreva.98.022114 · Cited by 33
Dynamics of Open Quantum Systems—Markovian Semigroups and Beyond
Czerwiński, A. (2022) · Symmetry · doi:10.3390/sym14081752 · Cited by 33
Tuning non-Markovianity by spin-dynamics control
Lorenzo, S., Plastina, F., & Paternostro, M. (2013) · Physical Review A · doi:10.1103/physreva.87.022317 · Cited by 33
Minimal evolution time and quantum speed limit of non-Markovian open systems
Meng, X., Wu, C., & Guo, H. M. (2015) · Scientific Reports · doi:10.1038/srep16357 · Cited by 34
Dynamics of initially correlated open quantum systems: Theory and applications
Paz-Silva, G. A., Hall, M. J. W., & Wiseman, H. M. (2019) · Physical Review A · doi:10.1103/physreva.100.042120 · Cited by 33
Gaussian interferometric power as a measure of continuous-variable non-Markovianity
Souza, L. A. M., Dhar, H. S., Bera, M. N., Liuzzo-Scorpo, P., & Adesso, G. (2015) · Physical Review A · doi:10.1103/physreva.92.052122 · Cited by 33
Switching quantum memory on and off
Franco, R. L. (2015) · New Journal of Physics · doi:10.1088/1367-2630/17/8/081004 · Cited by 32
Quantification of non-Markovian effects in the Fenna-Matthews-Olson complex
Mujica‐Martinez, C. A., Nalbach, P., & Thorwart, M. (2013) · Physical Review E · doi:10.1103/physreve.88.062719 · Cited by 32
Tensor power of dynamical maps and positive versus completely positive divisibility
Benatti, F., Chruściński, D., & Filippov, S. N. (2017) · Physical Review A · doi:10.1103/physreva.95.012112 · Cited by 32
Entanglement control in quantum networks by quantum-coherent time-delayed feedback
Hein, S. M., Schulze, F., Carmele, A., & Knorr, A. (2015) · Physical Review A · doi:10.1103/physreva.91.052321 · Cited by 32
How Quantum Evolution with Memory is Generated in a Time-Local Way
Nestmann, K., Bruch, V., & Wegewijs, M. R. (2021) · Physical Review X · doi:10.1103/physrevx.11.021041 · Cited by 33
Regula, B., Takagi, R., & Gu, M. (2021) · Quantum · doi:10.22331/q-2021-08-09-522 · Cited by 37
Entanglement distribution in optical fibers assisted by nonlocal memory effects
Xiang, G., Hou, Z., Li, C., Guo, G., Breuer, H., Laine, E.-M., & Piilo, J. (2014) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/107/54006 · Cited by 32
Giorgi, G. L., Galve, F., & Zambrini, R. (2015) · Physical Review A · doi:10.1103/physreva.92.022105 · Cited by 33
Thermodynamic fingerprints of non-Markovianity in a system of coupled superconducting qubits
Raja, S. H., Borrelli, M., Schmidt, R., Pekola, J. P., & Maniscalco, S. (2018) · Physical Review A · doi:10.1103/physreva.97.032133 · Cited by 32
Markovian semigroup from non-Markovian evolutions
Wudarski, F., & Chruściński, D. (2016) · Physical Review A · doi:10.1103/physreva.93.042120 · Cited by 31
Exact non-Markovian dynamics of qubits coupled to two interacting environments
Shen, H. Z., Li, D., Su, S., Zhou, Y. H., & Yi, X. X. (2017) · Physical Review A · doi:10.1103/physreva.96.033805 · Cited by 33
The interplay between local and non-local master equations: exact and approximated dynamics
Megier, N., Smirne, A., & Vacchini, B. (2020) · New Journal of Physics · doi:10.1088/1367-2630/ab9f6b · Cited by 30
Capacity of non-Markovianity to boost the efficiency of molecular switches
Spaventa, G., Huelga, S. F., & Plenio, M. B. (2022) · Physical Review A · doi:10.1103/physreva.105.012420 · Cited by 30
Self-citationDecoherence-assisted transport in quantum networks
Marais, A., Sinayskiy, I., Kay, A., Petruccione, F., & EKERT, A. K. (2013) · New Journal of Physics · doi:10.1088/1367-2630/15/1/013038 · Cited by 30
Quantum non-Markovianity induced by Anderson localization
Lorenzo, S., Lombardo, F., Ciccarello, F., & Palma, G. M. (2017) · Scientific Reports · doi:10.1038/srep42729 · Cited by 29
Temporal steering in four dimensions with applications to coupled qubits and magnetoreception
Ku, H.-Y., Chen, S.-L., Chen, H., Lambert, N., Chen, Y.-N., & Nori, F. (2016) · Physical Review A · doi:10.1103/physreva.94.062126 · Cited by 29
Non-Markovian quantum control as coherent stochastic trajectories
Sakuldee, F., Milz, S., Pollock, F. A., & Modi, K. K. (2018) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/aabb1e · Cited by 29
Experimental Investigation of Spectra of Dynamical Maps and their Relation to non-Markovianity
Yu, S., Wang, Y., Ke, Z., Liu, W., Meng, Y., Li, Z.-P., Zhang, W., Chen, G., Tang, J., Li, C., et al. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.060406 · Cited by 29
Chiriacò, G., Tsitsishvili, M., Poletti, D., Fazio, R., & Dalmonte, M. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.108.075151 · Cited by 29
Multispin probes for thermometry in the strong-coupling regime
Brenes, M., & Segal, D. (2023) · Physical Review A · doi:10.1103/physreva.108.032220 · Cited by 29
A measure of non-Markovianity for unital quantum dynamical maps
Haseli, S., Salimi, S., & Khorashad, A. S. (2015) · Quantum Information Processing · doi:10.1007/s11128-015-1052-7 · Cited by 29
Time-dependent transport in open systems based on quantum master equations
Knezevic, I., & Novakovic, B. (2013) · Journal of Computational Electronics · doi:10.1007/s10825-013-0474-7 · Cited by 29
Overview on the Phenomenon of Two-Qubit Entanglement Revivals in Classical Environments
Franco, R. L., & Compagno, G. (2017) · Quantum science and technology · doi:10.1007/978-3-319-53412-1_17 · Cited by 28
Controllable dissipation of a qubit coupled to an engineering reservoir
Shen, H. Z., Xu, S., Yi, S., & Yi, X. X. (2018) · Physical Review A · doi:10.1103/physreva.98.062106 · Cited by 29
Reimer, V., Wegewijs, M. R., Nestmann, K., & Pletyukhov, M. (2019) · The Journal of Chemical Physics · doi:10.1063/1.5094412 · Cited by 28
Rate Operator Unraveling for Open Quantum System Dynamics
Smirne, A., Caiaffa, M., & Piilo, J. (2020) · Physical Review Letters · doi:10.1103/physrevlett.124.190402 · Cited by 30
Quantum Metrology in the Noisy Intermediate‐Scale Quantum Era
Jiao, L., Wu, W., Bai, S., & An, J. (2023) · Advanced Quantum Technologies · doi:10.1002/qute.202300218 · Cited by 31
Threshold for nonthermal stabilization of open quantum systems
Cai, C. Y., Yang, L., & Sun, C. P. (2014) · Physical Review A · doi:10.1103/physreva.89.012128 · Cited by 28
Competition between memory-keeping and memory-erasing decoherence channels
Apollaro, T. J. G., Lorenzo, S., Franco, C. D., Plastina, F., & Paternostro, M. (2014) · Physical Review A · doi:10.1103/physreva.90.012310 · Cited by 28
Lankinen, J., Lyyra, H., Sokolov, B., Teittinen, J., Ziaei, B., & Maniscalco, S. (2016) · Physical Review A · doi:10.1103/physreva.93.052103 · Cited by 29
Non-Markovianity and Coherence of a Moving Qubit inside a Leaky Cavity
Mortezapour, A., Borji, M. A., Park, D., & Franco, R. L. (2017) · Open Systems & Information Dynamics · doi:10.1142/s1230161217400066 · Cited by 28
Amato, G., Breuer, H., & Vacchini, B. (2018) · Physical Review A · doi:10.1103/physreva.98.012120 · Cited by 27
Entanglement negativity as a universal non-Markovianity witness
Kołodyński, J., Rana, S., & Streltsov, A. (2020) · Physical Review A · doi:10.1103/physreva.101.020303 · Cited by 27
Metadata
- Authors
- Rivas, Á., Huelga, S. F., & Plenio, M. B.
- Affiliations
- University of Hertfordshire (GB)
- Universität Ulm (DE)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2010-07-28
- Volume
- 105
- Issue
- 5
- Pages
- 050403-050403
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2087654101
- Semantic Scholar
- 650d8d49ad99f9052b54cd06292f0aa97673ea14
- Cited by
- 1,037
- References
- 22
- Citations by year
- 2026: 67 · 2025: 83 · 2024: 63 · 2023: 59 · 2022: 67 · 2021: 73 · 2020: 75 · 2019: 72 · 2018: 62 · 2017: 68 · 2016: 67 · 2015: 64 · 2014: 69 · 2013: 50 · 2012: 58
- FWCI
- 49.75
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- University of Hertfordshire Research Archive (University of Hertfordshire) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Keywords
- non-Markovianity, quantum entanglement, open quantum systems, quantum correlations, non-Markovianity measures, quantum evolution, system-environment interaction, necessary and sufficient conditions, quantum state tomography
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 2026-10-06, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-06 (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
