Operators versus functions: from quantum dynamical semigroups to tomographic semigroups

21st International Conference on Integrable Systems and Quantum Symmetries

Aniello, Paolo^1

Dipartimento di Fisica, Università di Napoli Federico II, Complesso Universitario di Monte S. Angelo, via Cintia, 80126 Napoli, Italy^1

关键词: Classical probabilities;    Group-theoretical methods;    Quantum dynamical semigroup;    Quantum dynamical semigroups;    Quantum information science;    Semigroup of operators;    Semigroups of operators;    Theoretical framework;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/474/1/012005/pdf
DOI  :  10.1088/1742-6596/474/1/012005

来源: IOP

【 摘 要 】

Quantum mechanics can be formulated in terms of phase-space functions, according to Wigner's approach. A generalization of this approach consists in replacing the density operators of the standard formulation with suitable functions, the so-called generalized Wigner functions or (group-covariant) tomograms, obtained by means of group-theoretical methods. A typical problem arising in this context is to express the evolution of a quantum system in terms of tomograms. In the case of a (suitable) open quantum system, the dynamics can be described by means of a quantum dynamical semigroup 'in disguise', namely, by a semigroup of operators acting on tomograms rather than on density operators. We focus on a special class of quantum dynamical semigroups, the twirling semigroups, that have interesting applications, e.g., in quantum information science. The 'disguised counterparts' of the twirling semigroups, i.e., the corresponding semigroups acting on tomograms, form a class of semigroups of operators that we call tomographic semigroups. We show that the twirling semigroups and the tomographic semigroups can be encompassed in a unique theoretical framework, a class of semigroups of operators including also the probability semigroups of classical probability theory, so achieving a deeper insight into both the mathematical and the physical aspects of the problem.