Quantum entropies, Schur concavity and dynamical semigroups

24th International Conference on Integrable Systems and Quantum symmetries

Aniello, Paolo^1

Dipartimento di Fisica Ettore Pancini, Universita di Napoli Federico II, INFN-Sezione di Napoli, C.U. di Monte sant'Angelo, via Cintia, Napoli

I-80126, Italy^1

关键词: Completely positive;    Completely positive linear maps;    Initial conditions;    Open quantum systems;    Quantum information science;    Quantum setting;    Tsallis entropies;    Von Neumann entropy;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/804/1/012003/pdf
DOI  :  10.1088/1742-6596/804/1/012003

来源: IOP

【 摘 要 】

Entropy plays a fundamental role in several branches of physics. In the quantum setting, one usually considers the von Neumann entropy, but other useful quantities have been proposed in the literature; e.g., the Rényi and the Tsallis entropies. The evolution of an open quantum system, described by a semigroup of dynamical maps (in short, a dynamical semigroup), may decrease a quantum entropy, for some initial condition. We will discuss various characterizations of those dynamical semigroups that, for every initial condition, do not decrease a general class of quantum entropies, which is defined using the notion of Schur concavity of a function. We will not assume that such a dynamical semigroup be completely positive, the physical justification of this condition being controversial. Therefore, we will consider semigroups of trace-preserving, positive - but not necessarily completely positive - linear maps. We will next focus on a special class of (completely positive) dynamical semigroups, the twirling semigroups, having applications in quantum information science. We will argue that the whole class of dynamical semigroups that do not decrease a quantum entropy can be obtained as a suitable generalization of the twirling semigroups.