On Faces of the set of Quantum Channels

Abstract

A linear map $L$ from ${\mathbb{C}}^{n\times n}$ into ${\mathbb{C}}^{n\times n}$ is called a quantum channel if it is completely positive and trace preserving. The set ${\mathcal{L}}_n$ of all such quantum channels is known to be a compact convex set. While the extreme points of ${\mathcal{L}}_n$ can be characterized, not much is known about the structure of its higher dimensional faces. Using the so called Choi matrix $Z(L)$ associated with the quantum channel $L$, we compute the maximum dimension of a proper face of ${\mathcal{L}}_n$, and in addition the possible dimensions of faces generated by $L$ when $rankZ(L)=2$.

21 pages

References in corpus (1)

• Some Open Problems in Quantum Information Theory