近日，芬兰赫尔辛基大学的Marco Cattaneo及其研究团队取得一项新进展。经过不懈努力，他们对碰撞模型的强对称性和协变量子映射的物理膨胀进行研究。相关研究成果已于2025年2月6日在国际知名学术期刊《物理评论A》上发表。

本工作系统地探讨了量子映射的弱对称性在其膨胀中的表现形式。研究人员证明，对于各类物理膨胀，包括哈密顿量驱动的膨胀和模拟马尔可夫开放量子动力学的短时碰撞模型，弱对称性总是会导致膨胀演化中的强对称性，从而在系统-环境空间中产生守恒量。研究人员还利用克里洛夫子空间刻画了这些对称性产生的子空间。此外，研究人员展示了某些不同类型的物理膨胀对膨胀演化没有约束，因此不需要强对称性。最后，研究人员通过多个说明性和教学性的例子来补充他们的发现。

这项研究结果为构建量子映射的物理膨胀提供了基本指南，全面理解了对称性如何在实验室或量子计算机中塑造其实现方式。

据悉，量子映射在量子信息理论和开放量子系统中具有基础性地位。特别是协变或弱对称量子映射，在定义遵循热力学的量子演化、建立资源理论中的自由操作以及与量子参考系变换相一致的方面发挥着关键作用。为了在实验室中实现量子映射，通常需要设计一个物理膨胀，这对应于使系统与环境发生纠缠的幺正演化。

附：英文原文

Title: Strong symmetries in collision models and physical dilations of covariant quantum maps

Author: Marco Cattaneo

Issue&Volume: 2025/02/06

Abstract: Quantum maps are fundamental to quantum information theory and open quantum systems. Covariant or weakly symmetric quantum maps, in particular, play a key role in defining quantum evolutions that respect thermodynamics, establish free operations in resource theories, and are consistent with transformations of quantum reference frames. To implement quantum maps in the laboratory, one typically engineers a physical dilation, which corresponds to a unitary evolution entangling the system with an environment. This work systematically explores how weak symmetries of quantum maps manifest in their dilations. We demonstrate that for various classes of physical dilations, including Hamiltonian-driven dilations and short-time collision models that simulate Markovian open quantum dynamics, weak symmetries always lead to strong symmetries in the dilated evolution, resulting in conserved quantities in the system-environment space. We also characterize the subspace where these symmetries arise using Krylov subspaces. Moreover, we show that some different types of physical dilations have no constraints on the dilated evolution, requiring no strong symmetry. Finally, we complement our findings with a variety of illustrative and pedagogical examples. Our results provide essential guidelines for constructing physical dilations of quantum maps, offering a comprehensive understanding of how symmetries shape their implementations in a laboratory or on a quantum computer.

DOI: 10.1103/PhysRevA.111.022209

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.111.022209

来源：科学网  小柯机器人