Geometry of Generalized Depolarizing Channels

Details Geometry of Generalized Depolarizing Channels Geometry of Generalized Depolarizing Channels

2009-09-10

arxiv.org/abs/0909.1973v1

Phys. Rev. A 80, 042330 (2009)

Physics

Quantum Physics

11 pages, 1 figure

Scientific paper

10.1103/PhysRevA.80.042330

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.

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