Geometry of Generalized Depolarizing Channels
Quantum Physics
2009-11-04 v1
Abstract
A generalized depolarizing channel acts on an N-dimensional quantum system to compress the ``Bloch ball'' in N^2-1 directions; it has a corresponding compression vector. We investigate the geometry of these compression vectors and prove a conjecture of Dixit and Sudarshan [1], namely that when N=2^d (i.e. the system consists of d qubits) and we work in the Pauli basis then the set of all compression vectors forms a simplex. We extend this result by investigating the geometry in other bases; in particular we find precisely when the set of all compression vectors forms a simplex.
Cite
@article{arxiv.0909.1973,
title = {Geometry of Generalized Depolarizing Channels},
author = {Christian K. Burrell},
journal= {arXiv preprint arXiv:0909.1973},
year = {2009}
}
Comments
11 pages, 1 figure