Accessible maps in a group of classical or quantum channels

TitleAccessible maps in a group of classical or quantum channels
Publication TypeJournal Article
Year of Publication2022
AuthorsSadri K, Shahbeigi F, Puchała Z, Życzkowski K
JournalOpen Systems & Information Dynamics
Volume29
Start Page2250002
Date Published08/2022
Abstract

We study the problem of accessibility in a set of classical and quantum channels admitting a group structure. Group properties of the set of channels, and the structure of the closure of the analyzed group G plays a pivotal role in this regard. The set of all convex combinations of the group elements contains a subset of channels that are accessible by a dynamical semigroup. We demonstrate that accessible channels are determined by probability vectors of weights of a convex combination of the group elements, which depend neither on the dimension of the space on which the channels act, nor on the specific representation of the group. Investigating geometric properties of the set A of accessible maps we show that this set is non-convex, but it enjoys the star-shape property with respect to the uniform mixture of all elements of the group. We demonstrate that the set A covers a positive volume in the polytope of all convex combinations of the elements of the group.

URLhttps://doi.org/10.1142/S1230161222500020
DOI10.1142/S1230161222500020

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Data aktualizacji: 13/10/2022 - 09:53; autor zmian: Zbigniew Puchała (zbyszek@iitis.pl)