Avoiding Irreversibility: Engineering Resonant Conversions of Quantum Resources

Korzekwa, Kamil; Chubb, Christopher T.; Tomamichel, Marco

doi:10.1103/physrevlett.122.110403

Cited by 33 publications

(28 citation statements)

References 35 publications

(48 reference statements)

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“…Crucially, we have found that the correction term can vanish independently of n when a certain resonance condition between the initial and final states is satisfied. This opens the path to transformation reversibility beyond the asymptotic limit, the phenomenon that we discuss in detail in the accompanying paper [18].…”

Section: Discussionmentioning

confidence: 88%

“…Our results can be directly applied to the study of important problems such as entanglement distillation [16] or coherence dilution [17], but also allow one for a rigorous analysis of the irreversibility arising when finite-size resources are interconverted. Most intriguingly, we find that if a pair of states satisfies a particular resonance condition, one can achieve lossless interconversion, i.e., transformation that is arbitrarily close to reversible even for finite n. In the accompanying paper [18] we discuss how this effect can be employed to avoid irreversibility, which directly affects, e.g., the performance of heat engines working with finite-size working bodies [19]. This paper is structured in the following way.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Moderate deviation analysis of majorisation-based resource interconversion

Chubb

Korzekwa

Tomamichel

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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We consider the problem of interconverting a finite amount of resources within all theories whose single-shot transformation rules are based on a majorisation relation, e.g. the resource theories of entanglement and coherence (for pure state transformations), as well as thermodynamics (for energy-incoherent transformations). When only finite resources are available we expect to see a non-trivial trade-off between the rate rn at which n copies of a resource state ρ can be transformed into nrn copies of another resource state σ, and the error level ǫn of the interconversion process, as a function of n. In this work we derive the optimal trade-off in the so-called moderate deviation regime, where the rate of interconversion rn approaches its optimum in the asymptotic limit of unbounded resources (n → ∞), while the error ǫn vanishes in the same limit. We find that the moderate deviation analysis exhibits a resonance behaviour which implies that certain pairs of resource states can be interconverted at the asymptotically optimal rate with negligible error, even in the finite n regime.

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Section: Discussionmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Moderate deviation analysis of majorisation-based resource interconversion

Chubb

Korzekwa

Tomamichel

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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“…When catalytic transformations with correlations are allowed, the mathematical condition governing the feasibility of a transformation becomes a simple entropic condition. In the various resource theories listed in the table, p refers to different objects: for entanglement theory, it denotes the Schmidt coefficients; for coherence, the incoherent coefficients; and for thermodynamics, the block-diagonal energy coefficients (see, e.g., [33]). We have placed question marks in the table entries that have not been explored (to the best of our knowledge).…”

Section: Related Workmentioning

confidence: 99%

Relative entropy and catalytic relative majorization

Rethinasamy

Wilde

2020

Phys. Rev. Research

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Given two pairs of quantum states, a fundamental question in the resource theory of asymmetric distinguishability is whether there exists a quantum channel converting one pair to the other. In this work, we reframe this question in such a way that a catalyst can be used to help perform the transformation, with the only constraint on the catalyst being that its reduced state is returned unchanged, so that it can be used again to assist a future transformation. What we find here, for the special case in which the states in a given pair are commuting, and thus quasiclassical, is that this catalytic transformation can be performed if and only if the relative entropy of one pair of states is larger than that of the other pair. This result endows the relative entropy with a fundamental operational meaning that goes beyond its traditional interpretation in the setting of independent and identical resources. Our finding thus has an immediate application and interpretation in the resource theory of asymmetric distinguishability, and we expect it to find application in other domains.

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“…Although important insights have been obtained in trying to connect the information-theoretic and fluctuation theorem approaches [17,18], they have, so far, not been explicitly related to dissipation. Resource-theoretic analysis of dissipation was performed independently [19][20][21][22], where the authors investigated irreversibility of thermodynamic processes due to finite-size effects. However, these results were obtained for quasi-classical case of energy-incoherent states, and so they are not able to account for quantum effects that come into play when dealing with even smaller systems, when fluctuations around thermodynamic averages are no longer just thermal in their origin.…”

Section: Introductionmentioning

confidence: 99%

Fluctuation-dissipation relations for thermodynamic distillation processes

Biswas,

Junior,

Horodecki

et al. 2021

Preprint

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The fluctuation-dissipation theorem is a fundamental result in statistical physics that establishes a connection between the response of a system subject to a perturbation and the fluctuations associated with observables in equilibrium. Here we derive its version within a resource-theoretic framework, where one investigates optimal quantum state transitions under thermodynamic constraints. More precisely, for a fixed transformation error, we prove a relation between the minimal amount of free energy dissipated in a thermodynamic distillation process and the free energy fluctuations of the initial state of the system. Our results apply to initial states given by either asymptotically many identical pure systems or arbitrary number of independent energy-incoherent systems, and allow not only for a state transformation, but also for the change of Hamiltonian. The fluctuation-dissipation relations we derive enable us to find the optimal performance of thermodynamic protocols such as work extraction, information erasure and thermodynamically-free communication, up to second-order asymptotics in the number N of processed systems. We thus provide a first rigorous analysis of these thermodynamic protocols for quantum states with coherence between different energy eigenstates in the intermediate regime of large but finite N .

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Avoiding Irreversibility: Engineering Resonant Conversions of Quantum Resources

Cited by 33 publications

References 35 publications

Moderate deviation analysis of majorisation-based resource interconversion

Moderate deviation analysis of majorisation-based resource interconversion

Relative entropy and catalytic relative majorization

Fluctuation-dissipation relations for thermodynamic distillation processes

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