Comparison of quantum channels and statistical experiments

Jenčová, Anna

doi:10.1109/isit.2016.7541699

Cited by 11 publications

(19 citation statements)

References 35 publications

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“…The problem of characterizing statistical relations equivalent to degradability (and approximate degradability) has been considered before [11], [12], [13], [14], [15], [16], [17], [18], [19], but only in the classical-quantum scenario (i.e., that of Fig. 2).…”

Section: Main Result: Equivalence Relationsmentioning

confidence: 99%

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Comparison of noisy channels and reverse data-processing theorems

Buscemi

2017

2017 IEEE Information Theory Workshop (ITW)

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This paper considers the comparison of noisy channels from the viewpoint of statistical decision theory. Various orderings are discussed, all formalizing the idea that one channel is "better" than another for information transmission. The main result is an equivalence relation that is proved for classical channels, quantum channels with classical encoding, and quantum channels with quantum encoding.

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Section: Main Result: Equivalence Relationsmentioning

confidence: 99%

“…The implication (iii) =⇒ (i) has been proved, using various techniques and in various degrees of generality, in Refs. [13], [15], [16], [18], [19].…”

Section: Sketch Proof Of Theoremmentioning

confidence: 99%

Comparison of noisy channels and reverse data-processing theorems

Buscemi

2017

2017 IEEE Information Theory Workshop (ITW)

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“…We call a (possibly infinite) family of monotones a complete set of monotones if it fully characterizes the necessary and sufficient conditions for the existence of a free transformation. Such sets of monotones were discussed in several specific settings [25,26,32,[121][122][123][124][125][126][127][128][129][130][131], but no set of general conditions with a clear operational meaning was previously known to provide a comprehensive characterization of transformations in general resource theories.…”

Section: Complete Sets Of Monotonesmentioning

confidence: 99%

General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks

2019

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We establish an operational characterization of general convex resource theories -describing the resource content of not only states, but also measurements and channels, both within quantum mechanics and in general probabilistic theories (GPTs) -in the context of state and channel discrimination. We find that discrimination tasks provide a unified operational description for quantification and manipulation of resources by showing that the family of robustness measures can be understood as the maximum advantage provided by any physical resource in several different discrimination tasks, as well as establishing that such discrimination problems can fully characterize the allowed transformations within the given resource theory.Specifically, we introduce a quantifier of resourcefulness of a measurement in any GPT, the generalized robustness of measurement, and show that it admits an operational interpretation as the maximum advantage that a given measurement provides over resourceless measurements in all state discrimination tasks. In the special case of quantum mechanics, we connect discrimination problems with single-shot information theory by showing that the generalized robustness of any measurement can be alternatively understood as the maximal increase in one-shot accessible information when compared to free measurements. We introduce two different approaches to quantifying the resource content of a physical channel based on the generalized robustness measures, and show that they quantify the maximum advantage that a resourceful channel can provide in several classes of state and channel discrimination tasks. Furthermore, we endow another measure of resourcefulness of states, the standard robustness, with an operational meaning in general GPTs as the exact quantifier of the maximum advantage that a state can provide in binary channel discrimination tasks. Finally, we establish that several classes of channel and state discrimination tasks form complete families of monotones fully characterizing the transformations of states and measurements, respectively, under general classes of free operations. Our results establish a fundamental connection between the operational tasks of discrimination and core concepts of resource theories -the geometric quantification of resources and resource manipulation -valid for all physical theories beyond quantum mechanics with no additional assumptions about the structure of the GPT

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“…Therefore, in this case the condition id ⊗ E(ρ AB ) = σ AC becomes equivalent to the degradability of D into F, that is, F = E • D, and we denote it simply by F ≺ q D. Notice that notions equivalent to quantum majorization have previously been considered in Refs. [49][50][51][52][53] in the contexts of quantum statistics and quantum information theory.…”

Section: Definition Of Quantum Majorizationmentioning

confidence: 99%

Quantum majorization and a complete set of entropic conditions for quantum thermodynamics

et al. 2018

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What does it mean for one quantum process to be more disordered than another? Interestingly, this apparently abstract question arises naturally in a wide range of areas such as information theory, thermodynamics, quantum reference frames, and the resource theory of asymmetry. Here we use a quantum-mechanical generalization of majorization to develop a framework for answering this question, in terms of single-shot entropies, or equivalently, in terms of semi-definite programs. We also investigate some of the applications of this framework, and remarkably find that, in the context of quantum thermodynamics it provides the first complete set of necessary and sufficient conditions for arbitrary quantum state transformations under thermodynamic processes, which rigorously accounts for quantum-mechanical properties, such as coherence. Our framework of generalized thermal processes extends thermal operations, and is based on natural physical principles, namely, energy conservation, the existence of equilibrium states, and the requirement that quantum coherence be accounted for thermodynamically.

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Comparison of quantum channels and statistical experiments

Cited by 11 publications

References 35 publications

Comparison of noisy channels and reverse data-processing theorems

Comparison of noisy channels and reverse data-processing theorems

General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks

Quantum majorization and a complete set of entropic conditions for quantum thermodynamics

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