Spread quantum information in one-shot quantum state merging

Yamasaki, Hayata; Murao, Mio

doi:10.48550/arxiv.1903.03619

Cited by 1 publication

(3 citation statements)

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“…An asymptotically non-surviving separation has been recently discovered in Ref. [52] in a communication task of quantum state merging [53][54][55]. Reference [52] discloses this phenomena by proving the difference in the required amount of entanglement resources in achieving one-shot quantum state merging under one-way and two-way LOCC, while this difference ceases to exist in the conventional asymptotic quantum state merging.…”

Section: Introductionmentioning

confidence: 89%

“…[52] in a communication task of quantum state merging [53][54][55]. Reference [52] discloses this phenomena by proving the difference in the required amount of entanglement resources in achieving one-shot quantum state merging under one-way and two-way LOCC, while this difference ceases to exist in the conventional asymptotic quantum state merging. In contrast with this communication task, we here consider another resource-theoretic task that is known as assisted distillation of coherence [21][22][23].…”

Section: Introductionmentioning

confidence: 94%

“…In this section, we investigate a phenomena of asymptotically non-surviving separation [52] of the hierarchy, especially between 1-LQICC and QIP, in achieving an information-processing task, specifically, assisted distillation of coherence. The assisted distillation of coherence involves two parties A and B sharing some initial state, and A can perform an arbitrary quantum operation while B has a restriction in generating coherence.…”

Section: Asymptotically Non-surviving Separation Of Hierarchy In Assi...mentioning

confidence: 99%

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Hierarchy of quantum operations in manipulating coherence and entanglement

Yamasaki

Vijayan

Hsieh

2021

Quantum

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Quantum resource theory under different classes of quantum operations advances multiperspective understandings of inherent quantum-mechanical properties, such as quantum coherence and quantum entanglement. We establish hierarchies of different operations for manipulating coherence and entanglement in distributed settings, where at least one of the two spatially separated parties are restricted from generating coherence. In these settings, we introduce new classes of operations and also characterize those maximal, i.e., the resource-non-generating operations, progressing beyond existing studies on incoherent versions of local operations and classical communication and those of separable operations. The maximal operations admit a semidefinite-programming formulation useful for numerical algorithms, whereas the existing operations not. To establish the hierarchies, we prove a sequence of inclusion relations among the operations by clarifying tasks where separation of the operations appears. We also demonstrate an asymptotically non-surviving separation of the operations in the hierarchy in terms of performance of the task of assisted coherence distillation, where a separation in a one-shot scenario vanishes in the asymptotic limit. Our results serve as fundamental analytical and numerical tools to investigate interplay between coherence and entanglement under different operations in the resource theory.

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