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Quantum Algorithms

On Faces of the set of Quantum Channels

arXiv

Authors: Raphael Loewy

Year

2016

Paper ID

43516

Status

Preprint

Abstract Read

~2 min

Abstract Words

112

Citations

N/A

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 {cal L}_n of all such quantum channels is known to be a compact convex set. While the extreme points of {cal 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 {cal L}_n, and in addition the possible dimensions of faces generated by L when rank \ Z(L)=2.

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It adds a 2016 reference point for readers tracking recent quantum research.
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.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1609.05890 [2] arXiv https://arxiv.org/abs/1609.05890 [3] Publisher https://arxiv.org/abs/1609.05890

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