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Quantum coherence sets the quantum speed limit for mixed states

Open access
Mondal, Debasis, Datta, Chandan, Sazim, Sk·2016·Physics Letters A
DOI 10.1016/j.physleta.2015.12.015
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Abstract

Abstract We cast observable measure of quantum coherence as a resource to control the quantum speed limit (QSL) for unitary evolutions. For non-unitary evolutions, QSL depends on that of the state of the system and environment together. We show that the product of the time bound and the coherence (asymmetry) or the quantum part of the uncertainty behaves in a geometric way under partial elimination and classical mixing of states. These relations give a new insight into the quantum speed limit. We also show that our bound is experimentally measurable and is tighter than various existing bounds in the literature.

Verified 2026-10-06 · 38 references not checked yet

AI snapshot

Written from the paper’s full text.

TL;DR

The paper casts quantum coherence/asymmetry, quantified by Wigner–Yanase skew information, as a resource that sets the quantum speed limit for mixed states. It derives tighter, experimentally measurable bounds for unitary and general CPTP/Markovian evolutions and shows how the time–coherence product behaves under classical mixing and partial elimination.

Key findings

  • For unitary evolution, the quantum speed is bounded by the state’s coherence/asymmetry with respect to the Hamiltonian, \(Q(\rho,H)=-\frac12 \mathrm{Tr}[\sqrt{\rho},H]^2\); an operator that detects less coherence/asymmetry slows the evolution. The bound generalizes to time-dependent Hamiltonians via a time-averaged \(\sqrt{Q}\).
  • The product of the minimal evolution time and \(\sqrt{Q}\) decreases under classical mixing and partial elimination. For mixing, the paper reports \(U^H_{\gamma_1\gamma_2}\le \sqrt{p}\,U^H_{\rho_1\rho_2}+\sqrt{1-p}\,U^H_{\sigma_1\sigma_2}\), illustrated with \(U(\rho_1,\rho_2)=0.43\), \(U(\sigma_1,\sigma_2)=0.42\), and \(U(\gamma_1,\gamma_2)=0.34\) for \(p=1/3\).
  • The authors propose an interferometric method to measure the quantum \(H\)-coherence and the affinity \(A(\rho_1,\rho_2)=\mathrm{Tr}(\sqrt{\rho_1}\sqrt{\rho_2})\), using SWAP-operator measurements; they state this can also measure Uhlmann fidelity.
  • They claim the bound is tighter than several existing bounds, including Uhlmann-fidelity and del Campo et al. bounds. Example comparisons include \(\tau\ge 0.72\) versus \(0.71\) from [58] for \(a=3\pi/4\), \(m=0\), and another case giving \(\tau\ge 0.9\) versus \(1.09\) from [58]. For Markovian evolution in a squeezed vacuum channel, the bound improves relative to [36] as interaction time increases.

Methods

  • Theoretical derivation using the Fubini–Study metric for mixed states along a unitary orbit, purification in an extended Hilbert space, Wigner–Yanase skew information, affinity, and Bargmann angle; inequalities are derived for unitary, time-dependent, and CPTP/Markovian evolutions.
  • Experimental proposal: an interferometric network with controlled-Hadamard and controlled-SWAP operations to measure \(\mathrm{Tr}(\sigma_1\sigma_2)\) and \(-\mathrm{Tr}[\sigma_1,H]^2\), from which \(Q\) and affinity are computed.
  • Examples: a general single-qubit state evolving under \(U=e^{ia(\hat n\cdot\vec\sigma+\alpha I)/\hbar}\), and a two-level atom in a squeezed vacuum Markovian channel analyzed via a Lindbladian and damping basis.

Limitations

  • The paper states that using the unitary bound directly for non-unitary evolution “will not give tight limit”; a tighter bound requires the infinitesimal distance along the dynamical map. It also notes the bound may become tighter depending on the purity of the state.
  • No experimental implementation is reported; the interferometric measurement is proposed only (evident from the text).
  • Comparisons with prior bounds are limited to selected examples and specific prior works, with no broad numerical survey or proof of universal tightness across all states and evolutions (evident from the text).

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1016/j.physleta.2015.12.015

Cites

60 of 98 references verified0 citation errors · 0 not checkable

Statistics

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Claims the paper makes

0 of 39 cited sources checked · 0 supported · 0 flagged

  • Findingreasoning
    § 5. Speed limit under classical mixing and partial elimination of states · p. 5

    The product of the time bound and the quantum part of the uncertainty (or quantum coherence/asymmetry) obeys an inequality when a part of the system is discarded.

    “The inequality gives an insight on how the product of the time bound of the evolution and the quantum part of the uncertainty [52, 78] in energy or quantum coherence or asymmetry of the state with respect to the evolution operator behaves if a part of the system is discarded.”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [52] [52] S. Luo, Theor. Math. Phys. 143 , 681 (2005). -

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [78] [78] S. Luo, Proc. of the AMS Vol. 132 , Num. 3, Pages 885890; S. Luo, Phys. Rev. A. 72 , 042110 (2005). -

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • Rests on an assumption: The affinity between the reduced states is at least the affinity between the full states: A(ρa,σa) ≥ A(ρab,σab).
  • Findingreasoning
    § 3. Quantum speed limits for unitary evolution · p. 3

    For a time dependent Hamiltonian H(t), the inequality becomes τ ≥ ħ√2 cos^{-1} A(ρ1,ρ2) / √Q_τ(ρ1,H(t)), where √Q_τ is the time average of the quantum coherence or quantum part of the energy uncertainty.

    “For a time dependent Hamiltonian H ( t ) , the inequality in (8) becomes τ ≥ ℏ √ 2 cos -1 A ( ρ 1 ,ρ 2 ) √ Q τ ( ρ 1 ,H ( t )) , where √ Q τ ( ρ 1 , H ( t )) = 1 τ ∫ τ 0 √ Q ( ρ 1 , H ( t )) dt can be regarded as the time average of the quantum coherence or quantum part of the energy uncertainty.”
    Quote in the paperSubstantial claim
  • Findingreasoning
    § 3. Quantum speed limits for unitary evolution · p. 3

    For a system initially in the |+> state, evolution under Ux=e^{iσx t} produces no evolution in the projective Hilbert space because [|+><+|, σx]=0.

    “We consider a system with | + 〉 state. If we evolve the system by unitary operators U z = e iσ z t and U x = e iσ x t , the system will not evolve under U x with time in the projective Hilbert space. This is due to the fact that the state of the system is incoherent when measured with respect to the evolution operator σ x , i.e., [ | + 〉〈 + | , σ x ] = 0 .”
    Quote in the paperSubstantial claim
  • Findingcitation
    § 8. Example of speed limit for unitary evolution · p. 6

    For a=3π/4 and m=0, the Mandelstam and Tamm kind of bound given in [58] is 0.71.

    “whereas the Mandelstam and Tamm kind of bound given in [58] would be 0.71.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [58] [58] D. Mondal and A. K. Pati, arXiv:1403.5182v2 (2014). - source

      Not checked in the free run.

  • Findingown data
    § 8. Example of speed limit for unitary evolution · p. 6

    For a=3π/4 and m=0, the quantum time bound is τ ≥ 0.72 (with ħ=1=ω).

    “For a = 3 π 4 and m = 0 , the quantum time bound is given by τ ≥ 0 . 72 considering ( ℏ = 1 = ω )”
    Quote in the paperNot a substantial claim
  • Classified as probably not a substantial claim. 18
  • May combine two claims. 12
  • The quote only partly states this claim. 1

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingown data
    § 8. Example of speed limit for unitary evolution · p. 6

    Under ω=1=ħ, for the specified states, U(ρ1,ρ2)=0.43.

    “U ( ρ 1 , ρ 2 ) = 0 . 43 , U ( σ 1 , σ 2 ) = 0 . 42 and U ( γ 1 , γ 2 ) = 0 . 34”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingown data
    § 8. Example of speed limit for unitary evolution · p. 6

    The inequality in Eq. (9) is satisfied for the specified example.

    “which implies the inequality is satisfied.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingown data
    § 8. Example of speed limit for unitary evolution · p. 6

    Under ω=1=ħ, for the specified states, U(σ1,σ2)=0.42.

    “U ( ρ 1 , ρ 2 ) = 0 . 43 , U ( σ 1 , σ 2 ) = 0 . 42 and U ( γ 1 , γ 2 ) = 0 . 34”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingcitation
    § 6. Generalization · p. 5

    For α=2, the quantity T_l(ρ^α_1,H,ρ^α_2) gives a tighter bound than Eq. (8) and can be measured in the interferometry.

    “This quantity for α = 2 , gives not only a tighter bound (than (8) ) but can also be measured in the interferometry [50, 75].”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [50] [50] D. Girolami, Phys. Rev. Lett. 113 , 170401 (2014). -

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [75] [75] A. K. Ekert, C. M. Alves, D. K. L. Oi, M. Horodecki, P. Horodecki, and L. C. Kwek, Phys. Rev. Lett. 88 , 217901 (2002). -

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingown data
    § 8. Example of speed limit for unitary evolution · p. 6

    Under ω=1=ħ, for the specified states, U(γ1,γ2)=0.34.

    “U ( ρ 1 , ρ 2 ) = 0 . 43 , U ( σ 1 , σ 2 ) = 0 . 42 and U ( γ 1 , γ 2 ) = 0 . 34”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationreasoning
    § 10. Example of speed limit for Markovian evolution · p. 7

    The Lindbladian L describes a two level atom in a laser field subjected to an irreversible de-coherence by its environment.

    “Therefore, here, L describes a two level atom in a laser field subjected to an irreversible de-coherence by its environment.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § 9. Quantum speed limit for any general evolution · p. 6

    For the first time, Taddei et al. [35] and Campo et al. [36] extended the MT bound for any physical processes.

    “For the first time, Taddei et al.[35] and Campo et al. [36] extended the MT bound for any physical processes.”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [35] [35] M. M. Taddei, B. M. Escher, L. Davidovich, and R. L. de Matos Filho, Phys. Rev. Lett. 110 , 050402 (2013). -

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [36] [36] A. del Campo, I. L. Egusquiza, M. B. Plenio, and S. F. Huelga, Phys. Rev. Lett. 110 , 050403 (2013). -

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § 9. Quantum speed limit for any general evolution · p. 6

    In [58], QSL for arbitrary physical processes was shown to be related to the visibility of the interference pattern.

    “Later in [58], QSL for arbitrary physical processes was shown to be related to the visibility of the interference pattern.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [58] [58] D. Mondal and A. K. Pati, arXiv:1403.5182v2 (2014). - source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S4 (based).

    Interpretationnone given
    § 9. Quantum speed limit for any general evolution · p. 7

    Given dρt/dt = Lρt, d√ρt/dt = L√ρt is always true for positive square-root of the density matrix.

    “Because, given dρ t dt = L ρ t , d √ ρ t dt = L √ ρ t is always true for positive square-root of the density matrix and this can be shown using the same lines of approach as given for unitary evolution case.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Interpretationnone given
    § 6. Generalization · p. 5

    The paper's results can be generalized for more general evolutions, such as dynamical semi-group and quantum channel.

    “Our results here can also be generalized for more general evolutions, such as dynamical semi-group, quantum channel et cetera .”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation
    § 2. Metric along unitary orbit · p. 3

    The quantity -Tr[√ρ,H]^2 = 2Q(ρ,H) is the quantum part of the uncertainty, comes from the total energy uncertainty on pure states in the extended Hilbert space, and is related to the quantum coherence of the state.

    “The quantity -[ Tr [ √ ρ, H ] 2 ] = 2 Q ( ρ, H ) in Eq. (5) is nothing but the quantum part of the uncertainty as defined in [52] and comes from the total energy uncertainty (∆ H ) 2 on the pure states | Ψ AB 〉 in the extended Hilbert space H A ⊗H B . The quantity is also related to the quantum coherence of the state [50].”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [52] [52] S. Luo, Theor. Math. Phys. 143 , 681 (2005). -

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [50] [50] D. Girolami, Phys. Rev. Lett. 113 , 170401 (2014). -

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Interpretationnone given
    § 8. Example of speed limit for unitary evolution · p. 5

    The Hamiltonian H = ω(n·σ + αI) becomes positive semidefinite for α ≥ 1.

    “This Hamiltonian H becomes positive semidefinite for α ≥ 1 .”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Interpretationcitation
    § 11. Conclusion · p. 8

    Our bounds presented here can be generalized for CPTP evolutions or Markovian processes as well as non-Markovian processes.

    “Our bounds presented here can also be generalized for CPTP evolutions or Markovian processes as well as non-Markovian processes [82, 90].”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [82] [82] Y.-J. Zhang et al., Sci. Rep. 4 , 4890 (2014); -

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [90] [90] Xu Zhen-Yu and Zhu Shi-Qun, Chin. Phys. Lett. 31 , 020301 (2013); Z.-Y. Xu et al., Phys. Rev. A, 89 , 012307 (2014); C. Liu et al., Phys. Rev. A, 91 , 022102 (2015); L. Hou et al., J. Phys. A, 48 , 495302 (2015). -

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • May combine two claims.

    Interpretationnone given
    § 11. Conclusion · p. 8

    Both skew information and quantum affinity A(.,.) can indeed be measured in experiment by recasting them to some other measurable quantities of another properly mapped states.

    “Here, we show for the first time that both the quantities can indeed be measured (and the formalism can also be used to measure Uhlmann fidelity) in the experiment by recasting them to some other measurable quantities of another properly mapped states.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation
    § 1. Introduction · p. 2

    For unitary evolutions, the Fubini-Study metric for mixed states is the Wigner-Yanase skew information, which counts the quantum part of the uncertainty and is a good measure of quantum coherence or asymmetry.

    “For unitary evolutions, it is nothing but the Wigner-Yanase skew information [66], which only counts for the quantum part of the uncertainty [52] and a good measure of quantum coherence [50, 67] or asymmetry [68, 69, 70, 71], which classifies coherence [72] as a resource.”
    Quote in the paperSubstantial claim0 of 4 sources checked
    • cites [66] [66] E. P. Wigner and M. M. Yanase, Proc. Nat. Acad. Sci. USA, 49, 910 (1963). -

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [52] [52] S. Luo, Theor. Math. Phys. 143 , 681 (2005). -

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [50] [50] D. Girolami, Phys. Rev. Lett. 113 , 170401 (2014). -

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [67] [67] D. P. Pires, L. C. C´ eleri, and D. O. Soares-Pinto, Phys. Rev. A 91 , 042330 (2015). -

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • May combine two claims.

    Interpretationreasoning
    § 6. Generalization · p. 5

    The bound given by Eq. (13) may become tighter than that given by Eq. (8) depending on the purity of the state Tr(ρ^2_1) and can be measured in the experiment.

    “Therefore, the bound given by Eq. (13) may become tighter than that given by Eq. (8) depending on the purity of the state Tr ( ρ 2 1 ) and most importantly, can be measured in the experiment.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation
    § 7. Comparison with existing bounds · p. 5

    In [58], quantum speed limits in terms of visibility and phase shift in interferometry were derived and shown to be tighter than existing bounds then.

    “In [58], quantum speed limits in terms of visibility and the phase shift in the interferometry was derived and was shown to be tighter than the existing bounds then.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [58] [58] D. Mondal and A. K. Pati, arXiv:1403.5182v2 (2014). - source

      Not checked in the free run.

  • May combine two claims.

    Premisecitation
    § 7. Comparison with existing bounds · p. 5

    F(ρ1,ρ2) ≥ Tr(√ρ1√ρ2) and (∆H)ρ1 ≥ √FQ/2 ≥ √-Tr[√ρ1,H]^2.

    “because (∆ H ) ρ 1 ≥ √ F Q 2 ≥ √ -Tr [ √ ρ 1 , H ] 2 [78] and F ( ρ 1 , ρ 2 ) ≥ Tr ( √ ρ 1 √ ρ 2 )”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [78] [78] S. Luo, Proc. of the AMS Vol. 132 , Num. 3, Pages 885890; S. Luo, Phys. Rev. A. 72 , 042110 (2005). -

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Interpretationnone given
    § 3. Quantum speed limits for unitary evolution · p. 3

    The time bound in Eq. (8) can be generalized for a time dependent Hamiltonian H(t).

    “The time bound in Eq. (8) can easily be generalized for time dependent Hamiltonian H ( t ) .”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation
    § 6. Generalization · p. 5

    The denominator of T_l(ρ^2_1,H,ρ^2_2) is the lower bound of the H coherence, i.e., √(-1/2 Tr[ρ1,H]^2) ≤ √(-Tr[√ρ1,H]^2).

    “The denominator of the quantity T l ( ρ 2 1 , H, ρ 2 2 ) , is the lower bound of the H coherence, i.e., √ -1 2 Tr [ ρ 1 , H ] 2 ≤ √ -Tr [ √ ρ 1 , H ] 2 [50].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [50] [50] D. Girolami, Phys. Rev. Lett. 113 , 170401 (2014). -

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § 9. Quantum speed limit for any general evolution · p. 6

    The result of [36] was further improved by Zhang et al. [82] to provide a QSL for open systems with an initially mixed state.

    “The result of [36] was further improved [82] by Zhang et al . to provide a QSL for open systems with an initially mixed state.”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [36] [36] A. del Campo, I. L. Egusquiza, M. B. Plenio, and S. F. Huelga, Phys. Rev. Lett. 110 , 050403 (2013). -

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [82] [82] Y.-J. Zhang et al., Sci. Rep. 4 , 4890 (2014); -

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationnone given
    § 4. Experimental proposal · p. 3

    The formalism can also be used to measure the Uhlmann fidelity in the experiment.

    “This formalism can also be used to measure the Uhlmann fidelity in the experiment.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationnone given
    § 11. Conclusion · p. 8

    In this paper, we define a new role for quantum coherence or asymmetry as a resource and show that it can be used to control and manipulate the speed of quantum evolution.

    “In this paper, we define a new role for it as a resource and show that it can be used to control and manipulate the speed of quantum evolution.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationnone given
    § 10. Example of speed limit for Markovian evolution · p. 7

    The damping asymmetry between the u and v components is due to the presence of T3.

    “Here, the damping asymmetry between the u and v components is due to the presence of T 3 .”
    Quote in the paperNot a substantial claim

  • The quote only partly states this claim.

    Interpretationreasoning
    § 6. Generalization · p. 5

    A tighter and experimentally realizable time bound can be derived using the bound in Eq. (8).

    “A more tighter and experimentally realizable time bound can be derived using this bound.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation
    § 6. Generalization · p. 5

    The relative purity and the lower bound of the H-coherence both can be measured.

    “This is due to the fact that the relative purity [75, 76] and the lower bound of the H-coherence [50] both can be measured.”
    Quote in the paperSubstantial claim0 of 3 sources checked
    • cites [75] [75] A. K. Ekert, C. M. Alves, D. K. L. Oi, M. Horodecki, P. Horodecki, and L. C. Kwek, Phys. Rev. Lett. 88 , 217901 (2002). -

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [76] [76] K. Bartkiewicz, K. Lemr and A. Miranowicz, Phys. Rev. A 88 , 052104 (2013). -

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [50] [50] D. Girolami, Phys. Rev. Lett. 113 , 170401 (2014). -

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Classified as probably not a substantial claim.

    Premisecitation
    § 11. Conclusion · p. 9

    Our bound is based on the generalization of the Fubini-Study metric for mixed states motivated by [65].

    “Whereas, our bound is based on the generalization of the Fubini-Study metric for mixed states motivated by [65].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [65] [65] D. Mondal, arXiv:1503.04146 (2015). - source

      Not checked in the free run.

  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation
    § 11. Conclusion · p. 8

    In a recent paper [50], a protocol was proposed to measure a lower bound of skew information experimentally and was argued for why skew information itself cannot be measured.

    “In a recent paper [50], a protocol was proposed to measure a lower bound of skew information, given by -1 4 Tr [ ρ, H ] 2 , experimentally and was argued for, why skew information itself cannot be measured.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [50] [50] D. Girolami, Phys. Rev. Lett. 113 , 170401 (2014). -

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

28 of 28

  • The paper relies on this without support.

    Most existing quantum speed limit bounds are either not measurable in interference experiments or not tight enough to be effectively used in experiments.

    “Most of the bounds in the literature are either not measurable in the interference experiments or not tight enough. As a result, cannot be effectively used in the experiments on quantum metrology, quantum thermodynamics, quantum communication and specially in Unruh effect detection et cetera , where a small fluctuation in a parameter is needed to detect.”

  • The paper relies on this without support.

    Quantum coherence Q(ρ,H) does not increase under classical mixing of states.

    “We know that the quantum coherence of a state Q ( ρ, H ) = -1 2 Tr [ √ ρ, H ] 2 should not increase under classical mixing of states.”

  • The paper relies on this without support.

    The affinity between the reduced states is at least the affinity between the full states: A(ρa,σa) ≥ A(ρab,σab).

    “To prove it, we use the fact that A ( ρ a , σ a ) ≥ A ( ρ ab , σ ab ) .”

  • The paper relies on this without support.

    For the map Φ, Tr ρ^α_2 = Tr ρ^α_1.

    “considering the fact that Tr ρ α 2 = Tr ρ α 1”

  • The paper relies on this without support.

    Any CPTP evolution is equivalent to a unitary evolution in the extended Hilbert space.

    “We know that any CPTP evolution is equivalent to a unitary evolution in the extended Hilbert space.”

  • The paper relies on this without support.

    If the typical time scale of the environment is much smaller (larger) than that of the system, the system dynamics can be considered Markovian (nonMarkovian).

    “If the typical time scale of the environment is much smaller (larger) than that of the system, the system dynamics can be considered to be Markovian (nonMarkovian).”

  • The paper relies on this without support.

    The effect of environmental noise is inevitable in any information processing device.

    “The effect of environmental noise is inevitable in any information processing device.”
7 of 7

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 trace distance determines the maximum probability of successfully determining which of two states was prepared, given a single copy, when the states have equal prior probability.

    “As Helstrom has shown [47], the trace distance determines the maximum probability of successfully determining which of the states in the pair was prepared, given a single copy, when the states have equal prior probability of having been prepared.”

    From Quantum speed limits, coherence, and asymmetry (2016) · cites this paper as [47]

Cites

Flagged first, then by citations

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  14. Kossakowski, 1972, Bull. Acad. Polon. Sci. Math., 20, 1021
  15. Xu, 2013, Chin. Phys. Lett., 31
  16. Xu, 2014, Phys. Rev. A, 89
  17. Liu, 2015, Phys. Rev. A, 91

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Authors
Mondal, D., Datta, C., & Sazim, S.
Affiliations
  • Harish-Chandra Research Institute (IN)
  • Institute of Physics, Bhubaneshwar (IN)
Corresponding author
  • Mondal, Debasis
  • Datta, Chandan
  • Sazim, Sk
ORCID
Venue
Physics Letters A
Publisher
Elsevier BV
Published
2016-02
Volume
380
Issue
5-6
Pages
689-695
ISSN
0375-9601 (ISSN-L)
DOI
10.1016/j.physleta.2015.12.015
OpenAlex
W1934634809
Semantic Scholar
fc5b52bbd9c58c4dfa49c76145a4dda37cfed4ef
Cited by
113
References
96
Citations by year
2026: 2 · 2025: 8 · 2024: 11 · 2023: 14 · 2022: 14 · 2021: 11 · 2020: 11 · 2019: 6 · 2018: 8 · 2017: 16 · 2016: 12
FWCI
11.77
Type
journal article
Language
en
Open access
Licence
www.elsevier.com/tdm/userlicense/1.0/ (tdm)
Locations
  • Physics Letters A (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
  • World Academy of Science, Engineering and Technology, International Journal of Physical and Mathematical Sciences
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
Keywords
quantum speed limit, quantum coherence, mixed states, non-unitary evolution, quantum resource theory, quantum uncertainty, partial trace

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.

Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-06.

Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-06.

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 ›

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