Locally distinguishable maximally entangled states by two-way LOCC

Yang, Yinghui; Yuan, Jiangtao; Wang, Caihong; Geng, Shi-Jiao

doi:10.1007/s11128-020-02957-2

“…Note that each local measurement might involve a combination of measurements all performed in the same laboratory. Most results on LOCC round complexity involve quantum state discrimination problems and focus just on separating one-round versus two-round success rates [9][10][11][12][13][14][15][16]. Much more challenging is proving that a given task requires more than two rounds of LOCC to complete, and only a few results are known of this form.…”

Section: Introductionmentioning

confidence: 99%

The Round Complexity of Local Operations and Classical Communication (LOCC) in Random-Party Entanglement Distillation

Liu¹,

George²,

Chitambar³

2022

Preprint

0

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A powerful operational paradigm for distributed quantum information processing involves manipulating pre-shared entanglement by local operations and classical communication (LOCC). The LOCC round complexity of a given task describes how many rounds of classical communication are needed to complete the task. Despite some results separating one-round versus two-round protocols, very little is known about higher round complexities. In this paper, we revisit the task of one-shot random-party entanglement distillation as a way to highlight some interesting features of LOCC round complexity. We first show that for random-party distillation in three qubits, the number of communication rounds needed in an optimal protocol depends on the entanglement measure used; for the same fixed state some entanglement measures need only two rounds to maximize whereas others need an unbounded number of rounds. In doing so, we construct a family of LOCC instruments that require an unbounded number of rounds to implement. We then prove explicit tight lower bounds on the LOCC round number as a function of distillation success probability. Our calculations show that the original W-state random distillation protocol by Fortescue and Lo is essentially optimal in terms of round complexity.

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Quantum secret sharing scheme based on prime dimensional locally distinguishable states

Hu,

Li,

Wei

et al. 2024

Quantum Inf Process

0

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The Round Complexity of Local Operations and Classical Communication (LOCC) in Random-Party Entanglement Distillation

Liu,

George,

Chitambar

2023

Quantum

1

0

View full text Add to dashboard Cite

A powerful operational paradigm for distributed quantum information processing involves manipulating pre-shared entanglement by local operations and classical communication (LOCC). The LOCC round complexity of a given task describes how many rounds of classical communication are needed to complete the task. Despite some results separating one-round versus two-round protocols, very little is known about higher round complexities. In this paper, we revisit the task of one-shot random-party entanglement distillation as a way to highlight some interesting features of LOCC round complexity. We first show that for random-party distillation in three qubits, the number of communication rounds needed in an optimal protocol depends on the entanglement measure used; for the same fixed state some entanglement measures need only two rounds to maximize whereas others need an unbounded number of rounds. In doing so, we construct a family of LOCC instruments that require an unbounded number of rounds to implement. We then prove explicit tight lower bounds on the LOCC round number as a function of distillation success probability. Our calculations show that the original W-state random distillation protocol by Fortescue and Lo is essentially optimal in terms of round complexity.

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Locally distinguishable maximally entangled states by two-way LOCC

Cited by 3 publications

References 26 publications

The Round Complexity of Local Operations and Classical Communication (LOCC) in Random-Party Entanglement Distillation

The Round Complexity of Local Operations and Classical Communication (LOCC) in Random-Party Entanglement Distillation

Quantum secret sharing scheme based on prime dimensional locally distinguishable states

The Round Complexity of Local Operations and Classical Communication (LOCC) in Random-Party Entanglement Distillation

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