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

TL;DR

This paper constructs a class of quantum information channels using twisted convolution and analyzes their properties as one-parameter semigroups with unique generator features, expanding understanding of quantum dynamical systems.

Contribution

It introduces a new class of quantum channels via twisted convolution, characterizes their semigroup structure, and explores their generators with unbounded operators, extending quantum dynamical semigroup theory.

Findings

Constructed a semigroup of quantum channels using quantum characteristic functions.

Identified generators with unbounded operator coefficients not fitting standard forms.

Discussed open problems related to these quantum dynamical semigroups.

Abstract

Using the tool of quantum characteristic functions of n-mode states in the boson Fock space {\Gamma}(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.