Bidirectional classical communication cost of a bipartite quantum channel assisted by non-signalling correlations

• URL: http://arxiv.org/abs/2408.02506v1
• Date: Mon, 5 Aug 2024 14:30:50 GMT
• Title: Bidirectional classical communication cost of a bipartite quantum channel assisted by non-signalling correlations
• Authors: Chengkai Zhu, Xuanqiang Zhao, Xin Wang,
• Abstract summary: This paper investigates the bidirectional classical communication cost of simulating a bipartite quantum channel assisted by non-signalling correlations. We derive semidefinite programming (SDP) formulations for the one-shot exact bidirectional classical communication cost via non-signalling bipartite superchannels. Our results elucidate the role of non-locality in quantum communication and pave the way for exploring quantum reverse Shannon theory in bipartite scenarios.
• Score: 6.1108095842541
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Understanding the classical communication cost of simulating a quantum channel is a fundamental problem in quantum information theory, which becomes even more intriguing when considering the role of non-locality in quantum information processing. This paper investigates the bidirectional classical communication cost of simulating a bipartite quantum channel assisted by non-signalling correlations. Such non-signalling correlations are permitted not only across spatial dimension between the two parties but also along the temporal dimension of the channel simulation protocol. By introducing non-signalling superchannels, we derive semidefinite programming (SDP) formulations for the one-shot exact bidirectional classical communication cost via non-signalling bipartite superchannels. We further introduce a channel's bipartite conditional min-entropy as an efficiently computable lower bound on the asymptotic cost of bidirectional classical communication. Our results in both one-shot and asymptotic settings provide lower bounds on the entanglement-assisted simulation cost in scenarios where entanglement is available to the two parties and can be utilized across the timeline of the protocol. Numerical experiments demonstrate the effectiveness of our bounds in estimating communication costs for various quantum channels, showing that our bounds can be tight in different scenarios. Our results elucidate the role of non-locality in quantum communication and pave the way for exploring quantum reverse Shannon theory in bipartite scenarios.

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