中国科学院数学与系统科学学院Zijian Zhang团队近日实现了通过信道状态二象性量化量子信道的魔性资源。2025年5月13日出版的《物理评论A》杂志发表了这项成果。

根据著名的Gottesman-Knill定理，驱动通用量子计算需要魔性资源（非稳定性）。因此，量子态和量子信道的魔性资源的表征和量化是一个重要的问题。研究组提出了一种方法，通过利用信道状态对偶将量子信道转换为相应的Choi态，从量子态的量子信道构建量子信道魔性资源的量词。他们关注的是基于量子态特征函数（傅里叶变换）的魔性资源的特定量词。 

与通过离散维格纳函数定义的量词不同，这个量词对所有维度都有很好的定义，并且易于计算。它满足了一些理想的性质，并为量子信道的mana（离散维格纳函数的一种对数负性）提供了一个上限。使用这个量，研究组评估了一些典型量子信道的魔性资源量，并将其与一些现有的魔性资源生成功率的量词进行了比较。对于素数维系统中的退相通道，该魔性资源量词本质上表征了魔性资源的平均发电能力，而对于一般通道，它们则大不相同，并出现了一些具有挑战性的问题。

附：英文原文

Title: Quantifying magic resource for quantum channels via channel-state duality

Author: Xiaohui Li, Shunlong Luo, Zijian Zhang

Issue&Volume: 2025/05/13

Abstract: According to the celebrated Gottesman-Knill theorem, magic resource (nonstabilizerness) is necessary to drive universal quantum computation. Thus characterization and quantification of magic resource for quantum states and quantum channels are significant issues. In this work, we propose a method to construct quantifiers of magic resource for quantum channels from those for quantum states by employing the channel-state duality to convert quantum channels to the corresponding Choi states. We focus on a specific quantifier of magic resource based on characteristic functions (Fourier transforms) of quantum states. This quantifier is well defined for all dimensions and easy to calculate, as opposed to those defined via discrete Wigner functions. It satisfies some desirable properties and provides an upper bound to the mana (a kind of logarithmic negativity of discrete Wigner functions) of quantum channels. Using this quantity, we evaluate the amount of magic resource for some typical quantum channels and compare them with some existing quantifiers of generating-power of magic resource. For the dephasing channels in prime dimensional systems, our quantifier of magic resource essentially characterizes the average generating power of magic resource, while, for general channels, they are quite different and some challenging issues arise.

DOI: 10.1103/PhysRevA.111.052420

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.111.052420