Moderate Deviation Analysis for Classical Communication over Quantum Channels

Chubb, Christopher T.; Tan, Vincent Y. F.; Tomamichel, Marco

doi:10.1007/s00220-017-2971-1

Cited by 42 publications

(28 citation statements)

References 42 publications

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“…Our second-order expansion falls into a larger class of results known as small deviation bounds, in which we consider a fixed error threshold . Two natural extensions are to the regime of large deviations [62], in which a fixed rate is considered, and moderate deviations [63,64], in which the rate approaches its optimum and the error vanishes. Last, but not least, we expect that our treatment of approximate majorisation can be extended to cover other distance measures.…”

Section: Discussionmentioning

confidence: 99%

Beyond the thermodynamic limit: finite-size corrections to state interconversion rates

Chubb

Tomamichel

Korzekwa

2018

Quantum

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Thermodynamics is traditionally constrained to the study of macroscopic systems whose energy fluctuations are negligible compared to their average energy. Here, we push beyond this thermodynamic limit by developing a mathematical framework to rigorously address the problem of thermodynamic transformations of finite-size systems. More formally, we analyse state interconversion under thermal operations and between arbitrary energy-incoherent states. We find precise relations between the optimal rate at which interconversion can take place and the desired infidelity of the final state when the system size is sufficiently large. These so-called second-order asymptotics provide a bridge between the extreme cases of single-shot thermodynamics and the asymptotic limit of infinitely large systems. We illustrate the utility of our results with several examples. We first show how thermodynamic cycles are affected by irreversibility due to finite-size effects. We then provide a precise expression for the gap between the distillable work and work of formation that opens away from the thermodynamic limit. Finally, we explain how the performance of a heat engine gets affected when the working body is small. We find that while perfect work cannot generally be extracted at Carnot efficiency, there are conditions under which these finite-size effects vanish. In deriving our results we also clarify relations between different notions of approximate majorisation.

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Section: Discussionmentioning

confidence: 99%

Beyond the thermodynamic limit: finite-size corrections to state interconversion rates

Chubb

Tomamichel

Korzekwa

2018

Quantum

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“…In the following, we refer to this quantity simply as the relative variance. The relative variance has been shown to measure leading-order corrections to asymptotic results in (quantum) information theory [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41], but here we show that its role extends to the genuine single-shot setting. We do this from two points of view: First, we show that the relative variance quantifies single-shot corrections to possible state-transitions between quantum states.…”

Section: Introductionmentioning

confidence: 74%

The variance of relative surprisal as single-shot quantifier

Boes,

Ng,

Wilming

2020

Preprint

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The variance of (relative) surprisal (also known as varentropy) so far mostly plays a role in information theory as quantifying the leading order corrections to asymptotic i. i. d. limits. Here, we comprehensively study the use of it to derive single-shot results in (quantum) information theory. We show that it gives genuine sufficient and necessary conditions for approximate single-shot state-transitions in generic resource theories without the need for further optimization. We also clarify its relation to smoothed min-and max-entropies, and construct a monotone for resource theories using only the standard (relative) entropy and variance of (relative) surprisal. This immediately gives rise to enhanced lower bounds for entropy production in random processes. We establish certain properties of the variance of relative surprisal which will be useful for further investigations, such as uniform continuity and upper bounds on the violation of sub-additivity. Motivated by our results, we further derive a simple and physically appealing axiomatic single-shot characterization of (relative) entropy which we believe to be of independent interest. We illustrate our results with several applications, ranging from interconvertibility of ergodic states, over Landauer erasure to a bound on the necessary dimension of the catalyst for catalytic state transitions and Boltzmann's H-theorem.

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“…Other choices of γ lead to interesting interplays, such as (23), between the success probability and the extracted work. These different asymptotic scenarios are known as small, large, and moderate deviation regime in the context of information theory (see [41] and references therein).…”

Section: Disappearance Of Work Fluctuations For Systems In Contact Wimentioning

confidence: 99%

Collective operations can extremely reduce work fluctuations

Perarnau-Llobet

Uzdin

2019

New J. Phys.

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We consider work extraction from N copies of a quantum system. When the same work-extraction process is implemented on each copy, the relative size of fluctuations is expected to decay as N 1. Here, we consider protocols where the copies can be processed collectively, and show that in this case work fluctuations can disappear exponentially fast in N. As a consequence, a considerable proportion of the average extractable work  can be obtained almost deterministically by globally processing a few copies of the state. This is derived in the two canonical scenarios for work extraction: (i) in thermally isolated systems, where  corresponds to the energy difference between initial and passive states, known as the ergotropy, and (ii) in the presence of a thermal bath, where  is given by the free energy difference between initial and thermal states.

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Moderate Deviation Analysis for Classical Communication over Quantum Channels

Cited by 42 publications

References 42 publications

Beyond the thermodynamic limit: finite-size corrections to state interconversion rates

Beyond the thermodynamic limit: finite-size corrections to state interconversion rates

The variance of relative surprisal as single-shot quantifier

Collective operations can extremely reduce work fluctuations

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