山东大学于晓东团队近日研究了量子态的虚拟克隆。相关论文于2025年7月22日发表在《物理评论A》杂志上。

物理过程的固有局限性阻止了任意量子态的复制。即使科学家的目标只是克隆两个不同的量子态，这仍然是不可能的，除非它们相互正交。

为了克服这一限制，研究组提出了一种虚拟克隆协议，该协议绕过了量子不可克隆定理的限制。具体来说，研究组首先概述虚拟克隆的一般框架，并推导出能够同时克隆一组状态的虚拟操作存在的必要和充分的标准。随后，通过对虚拟克隆过程的仿真代价的分析，研究组证明了确定最优虚拟克隆协议的问题可以转化为一个半确定规划问题。最后，他们建立了虚拟克隆与状态歧视之间的联系，并由此导出了最优克隆成本的一般界。

附：英文原文

Title: Virtual cloning of quantum states

Author: Zhi-Hao Bi, Jing-Tao Qiu, Xiao-Dong Yu

Issue&Volume: 2025/07/22

Abstract: The inherent limitations of physical processes prevent the copying of arbitrary quantum states. Furthermore, even if we only aim to clone two distinct quantum states, it remains impossible unless they are mutually orthogonal. To overcome this limitation, we propose a virtual-cloning protocol that bypasses the restrictions imposed by the quantum no-cloning theorem. Specifically, we begin by outlining the general framework for virtual cloning and deriving a necessary and sufficient criterion for the existence of a virtual operation capable of simultaneously cloning a set of states. Subsequently, through an analysis of the simulation cost of the virtual-cloning process, we demonstrate that the problem of identifying an optimal virtual-cloning protocol can be cast as a semidefinite programming problem. Finally, we establish a connection between virtual cloning and state discrimination, from which universal bounds on the optimal cloning cost are derived.

DOI: 10.1103/4y3n-p641

Source: https://journals.aps.org/pra/abstract/10.1103/4y3n-p641