A Resource Theory of Quantum Measurements

Guff, Thomas; McMahon, Nathan A.; Sanders, Yuval R.; Gilchrist, Alexei

doi:10.48550/arxiv.1902.08490

Cited by 9 publications

(12 citation statements)

References 39 publications

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“…The resource theoretic framework has been applied to various kinds of quantities [3][4][5][6][7][8], as well as employed to extract common features shared by a wide class of resources [9][10][11][12][13][14][15][16][17][18][19][20][21]. Recently, the framework has been extended beyond the consideration of static resources attributed to quantum states to dynamic resources attributed to quantum measurements and channels, and it has been under active investigation [15][16][17][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39].…”

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confidence: 99%

Application of the Resource Theory of Channels to Communication Scenarios

2020

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We introduce a resource theory of channels relevant to communication via quantum channels, in which the set of constant channels, useless channels for communication tasks, are considered as free resources. We find that our theory with such a simple structure is useful to address important problems in quantum Shannon theoryin particular, we provide a converse bound for the one-shot non-signalling assisted classical capacity that leads to the first direct proof of the strong converse property for non-signalling assisted communication, as well as obtain the one-shot channel simulation cost with non-signalling assistance. Our results not only provide new perspectives to those problems, but also admit concise proofs of them, connecting the recently developed fields of resource theories to 'classic' problems in quantum information theory and shedding light on the validity of resource theories of channels as effective tools to attack practical problems.

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confidence: 99%

Application of the Resource Theory of Channels to Communication Scenarios

2020

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“…For example, V and W could be subject to their own channel resource theories. Furthermore, recent work on resource theories of measurements [98] could enable our theories whic have the B class of communication to be further dissected.…”

Section: Discussionmentioning

confidence: 99%

Resource theories of multi-time processes: A window into quantum non-Markovianity

Berk,

Garner,

Yadin

et al. 2019

Preprint

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We investigate the conditions under which an uncontrollable background processes may be harnessed by an agent to perform a task that would otherwise be impossible within their operational framework. This situation can be understood from the perspective of resource theory: rather than harnessing 'useful' quantum states to perform tasks, we propose a resource theory of quantum processes across multiple points in time. Uncontrollable background processes fulfil the role of resources, and a new set of objects called superprocesses, corresponding to operationally implementable control of the system undergoing the process, constitute the transformations between them. After formally introducing a framework for deriving resource theories of multi-time processes, we present a hierarchy of examples induced by restricting quantum or classical communication within the superprocess -corresponding to a client-server scenario. The resulting nine resource theories have different notions of quantum or classical memory as the determinant of their utility. Furthermore, one of these theories has a strict correspondence between non-useful processes and those that are Markovian and, therefore, could be said to be a true 'quantum resource theory of non-Markovianity'.

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“…Moreover, the general concept of quantum coherence encompasses previous notions of quantumness, e.g., quantum-optical nonclassicality as formulated by Glauber and others [21][22][23][24][25], and thereby renders it possible to distinguish classical interference phenomena from coherence effects genuine to quantum physics. * jan.sperling@uni-paderborn.de Except for some recent approaches with remarkable implications [26][27][28][29][30][31], the state-based approach to quantum coherence does not address the quantumness of measurement itself [32]. However, there can be no doubt that the understanding of the nature of measurements is vital to the fundamentals of physics and its practical applications, e.g., allowing us to implement measurement-based quantum computation [33,34].…”

Section: Introductionmentioning

confidence: 99%

Measuring coherence of quantum measurements

Cimini

Gianani

Sbroscia

et al. 2019

Phys. Rev. Research

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The superposition of quantum states lies at the heart of physics and has been recently found to serve as a versatile resource for quantum information protocols, defining the notion of quantum coherence. In this contribution, we report on the implementation of its complementary concept, coherence from quantum measurements. By devising an accessible criterion which holds true in any classical statistical theory, we demonstrate that noncommutative quantum measurements violate this constraint, rendering it possible to perform an operational assessment of the measurement-based quantum coherence. In particular, we verify that polarization measurements of a single photonic qubit, an essential carrier of one unit of quantum information, are already incompatible with classical, i.e., incoherent, models of a measurement apparatus. Thus, we realize a method that enables us to quantitatively certify which quantum measurements follow fundamentally different statistical laws than expected from classical theories and, at the same time, quantify their usefulness within the modern framework of resources for quantum information technology.

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A Resource Theory of Quantum Measurements

Cited by 9 publications

References 39 publications

Application of the Resource Theory of Channels to Communication Scenarios

Application of the Resource Theory of Channels to Communication Scenarios

Resource theories of multi-time processes: A window into quantum non-Markovianity

Measuring coherence of quantum measurements

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