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arXiv:1710.01565 · Physical Review A

Optimal convex approximations of quantum states

Massimiliano Federico Sacchi

Published Oct 18, 2017• 10 citations
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Abstract

We consider the problem of optimally approximating an unavailable quantum state $\ensuremath{\rho}$ by the convex mixing of states drawn from a set of available states ${{\ensuremath{\nu}}_{i}}$. The problem is recast to look for the least distinguishable state from $\ensuremath{\rho}$ among the convex set ${\ensuremath{\sum}}_{i}{p}_{i}{\ensuremath{\nu}}_{i}$, and the corresponding optimal weights ${{p}_{i}}$ provide the optimal convex mixing. We present the complete solution for the optimal convex approximation of a qubit mixed state when the set of available states comprises the three bases of the Pauli matrices.

DOI
10.1103/physreva.96.042325

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Comment on “Optimal convex approximations of quantum states”

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In a recent paper, M. F. Sacchi [Phys. Rev. A 96, 042325 (2017)] addressed the general problem of approximating an unavailable quantum state by the convex mixing of different available states. For the case of qubit mixed states, we show that the analytical solutions in some cases are invalid. In this Comment, we present complete analytical solutions for the optimal convex approximation. Our solutions can be viewed as correcting and supplementing the results in the aforementioned paper.

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