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arXiv:1301.6658 · IEEE Transactions on Information Theory

Minimum Relative Entropy for Quantum Estimation: Feasibility and General Solution

Mattia Zorzi, Francesco Ticozzi, Augusto Ferrante

Published Oct 17, 2013• 15 citations
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Abstract

We propose a general framework for solving quantum state estimation problems using the minimum relative entropy criterion. A convex optimization approach allows us to decide the feasibility of the problem given the data, find the maximal common kernel of all admissible states and, whenever necessary, to relax the constraints in order to allow for a physically admissible solution. Building on these results, the variational analysis can be completed ensuring existence and uniqueness of the optimum. The latter can then be computed by efficient standard algorithms for convex optimization, without resorting to approximate methods or restrictive assumptions on its rank.

DOI
10.1109/tit.2013.2286087

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We propose a general framework for solving quantum state estimation problems using the minimum relative entropy criterion. A convex optimization approach allows us to decide the feasibility of the problem given the data, find the maximal common kernel of all admissible states and, whenever necessary, to relax the constraints in order to allow for a physically admissible solution. Building on these results, the variational analysis can be completed ensuring existence and uniqueness of the optimum. The latter can then be computed by efficient standard algorithms for convex optimization, without resorting to approximate methods or restrictive assumptions on its rank.
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