One-Shot Manipulation of Entanglement for Quantum Channels

Kim, Ho-Joon; Lee, Soojoon; Lami, Ludovico; Plenio, Martin B.

doi:10.1109/tit.2021.3079938

Cited by 8 publications

(3 citation statements)

References 60 publications

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“…-During the completion of this manuscript we became aware of two related works, Ref. [117] by Kim et al and Ref. [118] by Yuan et al, where the authors independently obtained results overlapping with some of our findings.…”

Section: Acknowledgmentssupporting

confidence: 76%

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One-Shot Manipulation of Dynamical Quantum Resources

Regula

Takagi

2021

Phys. Rev. Lett.

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We develop a unified framework to characterize one-shot transformations of dynamical quantum resources in terms of resource quantifiers, establishing universal conditions for exact and approximate transformations in general resource theories. Our framework encompasses all dynamical resources represented as quantum channels, including those with a specific structure -such as boxes, assemblages, and measurements -thus immediately applying in a vast range of physical settings. For the particularly important manipulation tasks of distillation and dilution, we tighten the bounds further and show that our conditions become necessary and sufficient for broad classes of important theories. This enables an exact characterization of these fundamental tasks and establishes a precise connection between operational problems and resource monotones based on entropic divergences. We exemplify our results by considering explicit applications to: quantum communication, where we obtain exact expressions for one-shot quantum capacity and simulation cost assisted by no-signalling, separability-preserving, and positive partial transpose-preserving codes; as well as to nonlocality, contextuality, and measurement incompatibility, where we present an operational application of a number of relevant resource measures.

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Section: Acknowledgmentssupporting

confidence: 76%

“…We are also grateful to the authors of Refs. [117,118] for coordinating the submission of our works. B.R.…”

mentioning

confidence: 99%

One-Shot Manipulation of Dynamical Quantum Resources

Regula

Takagi

2021

Phys. Rev. Lett.

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“…imaginary [12,13]. Moreover, due to the generality of this framework, it has been applied to study quantum measurements and quantum channels, and various resource theories about quantum measurements and channels have been proposed, such as measurement simulability and incompatibility [14][15][16], measurement informativeness [17], measurement coherence [18,19], separable channels [20,21] and positive partial transpose (PPT) channels [22][23][24][25] in dynamic entanglement theory, the magic [26,27] and coherence [18,28] of quantum channels, and the quantum memory of channels [29]. These resource theories have greatly promoted the vigorous development of quantum information science.…”

Section: Introductionmentioning

confidence: 99%

Projective robustness for quantum channels and measurements and their operational significance

Ye¹,

Luo²,

Li³

et al. 2022

Laser Phys. Lett.

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Recently, the projective robustness of quantum states was introduced in (Regula 2022 Phys. Rev. Lett. 128 110505). This demonstrates that the projective robustness is a useful resource monotone and can comprehensively characterize the capabilities and limitations of probabilistic protocols that manipulate quantum resources deterministically. In this paper, we will extend the projective robustness to any convex resource theory of quantum channels and measurements. First, we introduce the projective robustness of quantum channels and prove that it satisfies some good properties, especially sub-multiplicativity under any free quantum process. Moreover, we show that the projective robustness of channels quantifies the maximal advantage that a given channel outperforms all free channels in the simultaneous discrimination and exclusion of a fixed-state ensemble. Second, we define the projective robustness of quantum measurements and prove that it exactly quantifies the maximal advantage that a given measurement outperforms all free measurements in the simultaneous discrimination and exclusion of two fixed-state ensembles. Finally, within a specific channel resource setting based on measurement incompatibility, we show that the projective robustness of quantum channels coincides with the projective robustness of measurement incompatibility.

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Catalysis of entanglement and other quantum resources

Datta,

Varun Kondra,

Miller

et al. 2023

Rep. Prog. Phys.

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In chemistry, a catalyst is a substance which enables a chemical reaction or increases its rate, while remaining unchanged in the process. Instead of chemical reactions, quantum catalysis enhances our ability to convert quantum states into each other under physical constraints. The nature of the constraints depends on the problem under study and can arise, e.g., from energy preservation. This article reviews the most recent developments in quantum catalysis and gives a historical overview of this research direction. We focus on the catalysis of quantum entanglement and coherence, and also discuss this phenomenon in quantum thermodynamics and general quantum resource theories. We review applications of quantum catalysis and also discuss the recent efforts on universal catalysis, where the quantum state of the catalyst does not depend on the states to be transformed. Catalytic embezzling is also considered, a phenomenon that occurs if the catalyst's state can change in the transition.

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One-Shot Manipulation of Entanglement for Quantum Channels

Cited by 8 publications

References 60 publications

One-Shot Manipulation of Dynamical Quantum Resources

One-Shot Manipulation of Dynamical Quantum Resources

Projective robustness for quantum channels and measurements and their operational significance

Catalysis of entanglement and other quantum resources

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