Dynamical Resources

Gour, Gilad; Scandolo, Carlo Maria

doi:10.48550/arxiv.2101.01552

Cited by 19 publications

(37 citation statements)

References 79 publications

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“…See appendix B of the supplementary material for the complete proof. We note here that the proof additionally provides the first operational interpretation of the dynamical monotones introduced in [20].…”

Section: Lemma 2 [21]mentioning

confidence: 85%

“…In the case of channel majorization, we find the unique asymptotically continuous classical channel entropy function. Additionally, we provide a first operational interpretation to the complete family of dynamical monotones introduced in [20]. Finally, the wide applicability of games of chance opens up opportunities to extend our work to the quantum world and operationally characterize the entropy of a quantum channel.…”

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confidence: 97%

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What is Entropy? A new perspective from games of chance

Brandsen,

Geng,

Gour

2021

Preprint

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Given entropy's central role in multiple areas of physics and science, one important task is to develop a systematic and unifying approach to defining entropy. Games of chance become a natural candidate for characterising the uncertainty of a physical system, as a system's performance in gambling games depends solely on the uncertainty of its output. In this work, we construct families of games which induce pre-orders corresponding to majorization, conditional majorization, and channel majorization. Finally, we provide operational interpretations for all pre-orders, show the relevance of these results to dynamical resource theories, and find the only asymptotically continuous classical dynamic entropy.

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Section: Lemma 2 [21]mentioning

confidence: 85%

mentioning

confidence: 97%

What is Entropy? A new perspective from games of chance

Brandsen,

Geng,

Gour

2021

Preprint

Self Cite

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“…This does not change the implemented superchannel [17]. Furthermore, it was shown in [18,Theorem 2] that all parameterizations ( V E , D) with minimal system size |S| are unique up to the choice of a unitary.…”

Section: Quantum Network and Superchannelsmentioning

confidence: 96%

Quantum Network Discrimination

Hirche¹

2021

Preprint

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Discrimination between objects, in particular quantum states, is one of the most fundamental tasks in (quantum) information theory. Recent years have seen significant progress towards extending the framework to point-to-point quantum channels. However, with technological progress the focus of the field is shifting to more complex structures: Quantum networks. In contrast to channels, networks allow for intermediate access points where information can be received, processed and reintroduced into the network. In this work we study the discrimination of quantum networks and its fundamental limitations.In particular when multiple uses of the network are at hand, the rooster of available strategies becomes increasingly complex. The simplest quantum network that capturers the structure of the problem is given by a quantum superchannel. We discuss the available classes of strategies when considering n copies of a superchannel and give fundamental bounds on the asymptotically achievable rates in an asymmetric discrimination setting. Furthermore, we discuss achievability, symmetric network discrimination, the strong converse exponent, generalization to arbitrary quantum networks and finally an application to an active version of the quantum illumination problem.

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“…Importantly, we can impose additional structures to channels under study so that the resulting resource theory can describe various settings involving quantum channels with pre-determined structures, such as the scenario of Bell non-locality represented by non-signalling boxes [66][67][68], and measurement incompatibility [69], where a channel describes a set of POVMs [59]. Although the performance of channel distillation and one-shot channel manipulation in general re-source theories has recently been studied [54,55,59,63,64], the relation between the one-shot distillable resource and resource cost under arbitrary free channel transformations has still been elusive.…”

Section: Introductionmentioning

confidence: 99%

One-Shot Yield-Cost Relations in General Quantum Resource Theories

Takagi,

Regula,

Wilde

2021

Preprint

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Although it is well known that the amount of resources that can be asymptotically distilled from a quantum state or channel does not exceed the resource cost needed to produce it, the corresponding relation in the non-asymptotic regime is not well understood. Here, we establish a quantitative relation between the one-shot distillable resource yield and dilution cost in terms of transformation errors involved in these processes. Notably, our bound is applicable to quantum state and channel manipulation with respect to any type of quantum resource and any class of free transformations thereof, encompassing broad types of settings, including entanglement, quantum thermodynamics, quantum communication, and Bell non-locality. We also show that our techniques provide strong converse bounds relating the distillable resource and resource dilution cost in the asymptotic regime. Moreover, we introduce a class of channels that generalize twirling maps encountered in many resource theories, and by directly connecting it with resource quantification, we compute analytically several smoothed resource measures and improve our one-shot yield-cost bound in relevant theories. We use these operational insights to exactly evaluate important measures for various resource states in the resource theory of magic states.

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Dynamical Resources

Cited by 19 publications

References 79 publications

What is Entropy? A new perspective from games of chance

What is Entropy? A new perspective from games of chance

Quantum Network Discrimination

One-Shot Yield-Cost Relations in General Quantum Resource Theories

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