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Open Quantum Systems Decoherence
A review of matrix scaling and Sinkhorn's normal form for matrices and positive maps
arXiv
Authors: Martin Idel
Year
2016
Paper ID
43455
Status
Preprint
Abstract Read
~2 min
Abstract Words
103
Citations
N/A
Abstract
Given a nonnegative matrix A, can you find diagonal matrices D1, D2 such that D1AD2 is doubly stochastic? The answer to this question is known as Sinkhorn's theorem. It has been proved with a wide variety of methods, each presenting a variety of possible generalisations. Recently, generalisations such as to positive maps between matrix algebras have become more and more interesting for applications. This text gives a review of over 70 years of matrix scaling. The focus lies on the mathematical landscape surrounding the problem and its solution as well as the generalisation to positive maps and contains hardly any nontrivial unpublished results.
Why This Paper Matters
- This paper contributes to the Open Quantum Systems & Decoherence research area in the Quantum Articles archive.
- It adds a 2016 reference point for readers tracking recent quantum research.
- Given a nonnegative matrix A, can you find diagonal matrices D1, D2 such that D1AD2 is doubly stochastic?
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