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

• URL: http://arxiv.org/abs/2204.00781v3
• Date: Thu, 30 Mar 2023 20:24:08 GMT
• Title: The Round Complexity of Local Operations and Classical Communication (LOCC) in Random-Party Entanglement Distillation
• Authors: Guangkuo Liu, Ian George, Eric Chitambar
• Abstract summary: A powerful operational paradigm for distributed quantum information processing involves manipulating pre-shared entanglement. The LOCC round complexity of a given task describes how many rounds of classical communication are needed to complete the task. We 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.
• Score: 4.211128681972148
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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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