近日，日本京都大学的Masataka Yamada与日本明治学院大学的Takayuki Miyadera合作并取得一项新进展。他们揭示了一般概率论中量子信道的不相容。相关研究成果已于2024年12月10日在国际知名学术期刊《物理评论A》上发表。

据悉，在量子理论中，存在着无法同时执行的操作集，这些操作集被称为不相容操作集。虽然不相容性的这一定义可扩展至一般概率理论（GPTs），但相容集对复合系统定义的依赖性尚未得到深入研究。对于量子信道而言，其相容性是基于传统复合系统的希尔伯特空间张量积来定义的。然而，在GPTs中，复合系统的定义并非唯一，状态集可从最小张量变化到最大张量。

在本文中，除了通常的量子相容性外，研究人员还引入了效应空间复合系统中的最小张量相容性，并利用量子比特上的噪声恒等信道研究了它们之间的关系。结果发现，最小张量相容信道对的集合严格大于量子相容信道对的集合。

此外，研究人员从操作角度引入了几乎量子相容信道对的概念。这一概念对应于在相容性验证中，相关函数可以通过一个信道和效应的局部重新解释来实现的情况。研究人员证明，所有几乎量子相容信道对的集合，严格小于所有最小张量相容信道对的集合。

附：英文原文

Title: Incompatibility of quantum channels in general probabilistic theories

Author: Masataka Yamada, Takayuki Miyadera

Issue&Volume: 2024/12/10

Abstract: In quantum theory, sets of operations that cannot be performed simultaneously exist. These sets of operations are referred to as incompatible. While this definition of incompatibility extends to general probabilistic theories (GPTs), the dependence of the set of compatible sets on the definition of composite systems has not been thoroughly investigated. For quantum channels, compatibility is defined using the tensor product of Hilbert spaces based on the conventional composite system. However, in GPTs, composite systems are not uniquely defined, and the set of states can vary from the minimal tensor to the maximal tensor. In this paper, in addition to the usual quantum compatibility, we introduce min-tensor compatibility using the minimal tensor in the composite system of effect spaces and investigate their relationship employing noisy identity channels on qubits. As a result, we find that the set of min-tensor-compatible channel pairs is strictly broader than the set of quantum-compatible channel pairs. Furthermore, we introduce the concept of almost-quantum-compatible pairs of channels from an operational perspective. This concept corresponds to cases where the correlation functions in the verification of compatibility can be realized through a channel and local reinterpretation of effects. We demonstrate that the set of all almost-quantum-compatible channel pairs is strictly narrower than the set of all min-tensor-compatible channel pairs.

DOI: 10.1103/PhysRevA.110.062210

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.062210