Gielerak Roman, Wiśniewska Joanna, Sawerwain Marek
Institute of Control & Computation Engineering, University of Zielona Góra, Licealna 9, 65-417 Zielona Góra, Poland.
Institute of Information Systems, Faculty of Cybernetics, Military University of Technology, Gen. S. Kaliskiego 2, 00-908 Warszaw, Poland.
Entropy (Basel). 2024 Dec 9;26(12):1070. doi: 10.3390/e26121070.
Infinite-dimensional systems play an important role in the continuous-variable quantum computation model, which can compete with a more standard approach based on qubit and quantum circuit computation models. But, in many cases, the value of entropy unfortunately cannot be easily computed for states originating from an infinite-dimensional Hilbert space. Therefore, in this article, the unified quantum entropy (which extends the standard von Neumann entropy) notion is extended to the case of infinite-dimensional systems by using the Fredholm determinant theory. Some of the known (in the finite-dimensional case) basic properties of the introduced unified entropies were extended to this case study. Certain numerical examples for computing the proposed finite- and infinite-dimensional entropies are outlined as well, which allowed us to calculate the entropy values for infinite Hilbert spaces.
无限维系统在连续变量量子计算模型中发挥着重要作用，该模型可以与基于量子比特和量子电路计算模型的更标准方法相竞争。但是，在许多情况下，不幸的是，对于源自无限维希尔伯特空间的态，熵的值不容易计算。因此，在本文中，通过使用弗雷德霍姆行列式理论，将统一量子熵（它扩展了标准冯·诺依曼熵）的概念扩展到无限维系统的情况。所引入的统一熵在有限维情况下的一些已知基本性质也扩展到了本案例研究中。还概述了一些用于计算所提出的有限维和无限维熵的数值示例，这使我们能够计算无限希尔伯特空间的熵值。
