Minimum Relative Entropy for Quantum Estimation: Feasibility and General Solution

TL;DR

This paper introduces a convex optimization framework for quantum state estimation using minimum relative entropy, enabling feasible, unique solutions without restrictive assumptions, and providing efficient computational methods.

Contribution

It presents a general, convex optimization-based approach for quantum state estimation that guarantees feasibility, existence, and uniqueness of solutions, improving upon prior methods.

Findings

Feasibility of quantum state estimation can be efficiently decided.

Unique solutions can be computed using standard convex optimization algorithms.

The framework relaxes constraints to ensure physically admissible solutions.

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 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 standard, efficient standard algorithms for convex optimization, without resorting to approximate methods or restrictive assumptions on its rank.