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Open Quantum Systems Decoherence

There are many more positive maps than completely positive maps

arXiv
Authors: Igor Klep, Scott McCullough, Klemen Šivic, Aljaž Zalar

Year

2016

Paper ID

42486

Status

Preprint

Abstract Read

~2 min

Abstract Words

82

Citations

N/A

Abstract

A linear map between matrix spaces is positive if it maps positive semidefinite matrices to positive semidefinite ones, and is called completely positive if all its ampliations are positive. In this article quantitative bounds on the fraction of positive maps that are completely positive are proved. A main tool are real algebraic geometry techniques developed by Blekherman to study the gap between positive polynomials and sums of squares. Finally, an algorithm to produce positive maps which are not completely positive is given.

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  • A linear map between matrix spaces is positive if it maps positive semidefinite matrices to positive semidefinite ones, and is called completely positive if all its ampliations...

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