AI 中文总结
本研究针对有限维希尔伯特空间上不同输入输出维度的可逆量子信道，从多视角给出二十一种等价刻画，推导Choi态的三种等价表示，为相关应用提供综合框架。
AI 中文摘要
可逆量子信道在量子动力学和量子信息处理中具有基础性作用。若存在另一个量子信道作为其左逆，则该量子信道是可逆的。由于其内在重要性和广泛应用，从不同视角刻画可逆量子信道是必要的。本研究针对有限维希尔伯特空间上的可逆量子信道，特别关注输入与输出维度不同的情形，从代数、几何和信息论视角系统给出了可逆量子信道的二十种等价刻画。其中部分刻画是熟知的，部分是文献中隐含的或在其他语境中表述的，本研究对其进行了澄清；本研究还推导了Choi态刻画，具体证明了可逆量子信道的Choi态具有谱、直和、张量积三种等价形式。这二十一种等价刻画为可逆量子信道建立了综合框架，提供了关于量子信道结构和信息论性质的多样见解，并促进了可逆性在量子纠错、量子隐形传态、量子热力学等量子信息处理中的应用。
英文摘要
Reversible quantum channels play a fundamental role in quantum dynamics and quantum information processing. A quantum channel is reversible if there exists another quantum channel acting as its left inverse. Due to their intrinsic significance and wide applications, it is desirable to characterize reversible quantum channels from diverse perspectives. In this work, we study reversible quantum channels on finite-dimensional Hilbert spaces, with particular emphasis on the case of different input and output dimensions. We systematically present twenty-one equivalent characterizations of reversible quantum channels from algebraic, geometrical, and information-theoretical perspectives. Among these characterizations, some are well known, while others, implicit in the literature or formulated in other contexts, are clarified here; the Choi-state characterization is derived in this work. Specifically, we prove that the Choi states of reversible quantum channels admit three equivalent forms: the spectral, direct-sum, and tensor-product representations. These twenty-one equivalent characterizations establish a comprehensive framework for reversible quantum channels, provide diverse insights into the structural and information-theoretic properties of quantum channels, and facilitate applications of reversibility in quantum information processing such as quantum error correction, quantum teleportation, and quantum thermodynamics.
