发表机构
Politecnico di Milano（米兰理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究分析连续变量量子系统上的高斯量子马尔可夫半群的正则化与不可约性，建立相关代数准则，发现其不可约性强于正则化条件，为量子马尔可夫半群研究提供框架。
AI 中文摘要
我们研究作用于连续变量量子系统的高斯量子马尔可夫半群（GQMSs）的正则化与不可约性性质。首先，我们确定了该场景下算子的自然正则性概念，这使我们能够根据包含漂移项和量子扩散矩阵的代数条件，表述和刻画GQMSs的平滑效应。这些条件建立了与量子线性系统可控性理论以及无消相干子系统结构的联系。随后，我们通过几个等价的代数准则刻画不可约性：一个基于漂移项和量子扩散矩阵，一个基于生成元的广义GKLS表示中出现的算子，第三个由霍尔曼德条件的量子类比给出。一个核心且略显意外的结论是，与经典情形相反，不可约性严格强于确保正则化的条件。我们的结果为分析这些性质提供了代数框架，并为更广泛研究可约高斯量子马尔可夫半群，以及更一般的连续变量系统上的相关量子马尔可夫半群奠定了基础。
英文摘要
We study regularisation and irreducibility properties of Gaussian quantum Markov semigroups (GQMSs) acting on continuous-variable quantum systems. We first identify a natural notion of regularity for operators in this setting, which allows us to formulate and characterise the smoothing effects of GQMSs in terms of algebraic conditions involving the drift and quantum diffusion matrices. These conditions establish a connection with the controllability theory of quantum linear systems and with the structure of decoherence-free subsystems. We then characterise irreducibility through several equivalent algebraic criteria: one formulated in terms of the drift and quantum diffusion matrices, one in terms of the operators appearing in the generalised GKLS representation of the generator, and a third given by a quantum analogue of Hörmander's condition. A central and somewhat surprising consequence is that, in contrast with the classical case, irreducibility is strictly stronger than conditions ensuring regularisation. Our results provide an algebraic framework for analysing these properties and lay the groundwork for a broader study of reducible Gaussian quantum Markov semigroups and, more generally, more general relevant quantum Markov semigroups on continuous-variable systems.
Comments32 pages, comments and remarks are welcome
