Twisted convolution quantum information channels, one-parameter semigroups and their generators

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2022-02-27 DOI:10.1142/s0219025722400069

K. Parthasarathy

引用次数: 0

Abstract

Using the tool of quantum characteristic functions of n -mode states in the boson Fock space Γ( C n ) we construct a semigroup of quantum information channels. This leads to a special class of one-parameter semigroups of such channels. These semigroups are concrete but their generators have unbounded operator coeﬃcients. These one-parameter semigroups are also quantum dynamical semigroups and the form of the generators involve additional features which do not appear in the standard GKSL form. A heuristic discussion of the form of these generators is included. In the wake of this analysis many open problems arise naturally.

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扭曲卷积量子信息信道，单参数半群及其产生

利用玻色子Fock空间Γ(cn)中n模态的量子特征函数，构造了一个量子信息通道半群。这就产生了一类特殊的单参数信道半群。这些半群是具体的，但它们的生成器具有无界算子系数。这些单参数半群也是量子动力学半群，生成子的形式涉及标准GKSL形式中没有出现的附加特征。对这些生成器的形式进行了启发式讨论。在这种分析之后，自然出现了许多悬而未决的问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Infinite Dimensional Analysis Quantum Probability and Related Topics 数学-统计学与概率论

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： In the past few years the fields of infinite dimensional analysis and quantum probability have undergone increasingly significant developments and have found many new applications, in particular, to classical probability and to different branches of physics. The number of first-class papers in these fields has grown at the same rate. This is currently the only journal which is devoted to these fields. It constitutes an essential and central point of reference for the large number of mathematicians, mathematical physicists and other scientists who have been drawn into these areas. Both fields have strong interdisciplinary nature, with deep connection to, for example, classical probability, stochastic analysis, mathematical physics, operator algebras, irreversibility, ergodic theory and dynamical systems, quantum groups, classical and quantum stochastic geometry, quantum chaos, Dirichlet forms, harmonic analysis, quantum measurement, quantum computer, etc. The journal reflects this interdisciplinarity and welcomes high quality papers in all such related fields, particularly those which reveal connections with the main fields of this journal.