Optimal unilocal virtual quantum broadcasting

• URL: http://arxiv.org/abs/2310.15156v3
• Date: Thu, 25 Jul 2024 14:30:10 GMT
• Title: Optimal unilocal virtual quantum broadcasting
• Authors: Hongshun Yao, Xia Liu, Chengkai Zhu, Xin Wang,
• Abstract summary: We introduce protocols that can be approximated using physical operations with minimal cost. We formalize the simulation cost of a virtual quantum broadcasting protocol into a semidefinite programming problem.
• Score: 5.80377843790023
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum broadcasting is central to quantum information processing and characterizes the correlations within quantum states. Nonetheless, traditional quantum broadcasting encounters inherent limitations dictated by the principles of quantum mechanics. In a previous study, Parzygnat et al. [Phys. Rev. Lett. 132, 110203 (2024)] introduced a canonical broadcasting quantum map that goes beyond the quantum no-broadcasting theorem through a virtual process. In this work, we generalize the concept of virtual broadcasting to unilocal broadcasting by incorporating a reference system and introduce protocols that can be approximated using physical operations with minimal cost. First, we propose a universal unilocal protocol enabling multiple parties to share the correlations of a target bipartite state, which is encoded in the expectation value for any observable. Second, we formalize the simulation cost of a virtual quantum broadcasting protocol into a semidefinite programming problem. Notably, we propose a specific protocol with optimal simulation cost for the 2-broadcasting scenario, revealing an explicit relationship between simulation cost and the quantum system's dimension. Moreover, we establish upper and lower bounds on the simulation cost of the virtual $n$-broadcasting protocol and demonstrate the convergence of the lower bound to the upper bound as the quantum system's dimension increases.

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