Optimal convex approximations of quantum states

Abstract

We consider the problem of optimally approximating an unavailable quantum state $\rho$ by the convex mixing of states drawn from a set of available states $\{{\nu }_i\}$. The problem is recast to look for the least distinguishable state from $\rho$ among the convex set ${\sum }_i{p}_i{\nu }_i$, 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.

5 pages; 2 figures; added the section 'Addendum' and a reference to X.-B. Liang, B. Li, and S.-M. Fei, Phys. Rev. A 99, 016301 (2019), which corrects some results of Sec. III

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• The Quantum Chernoff Bound
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• Trace-distance measure of coherence
• The Fidelity and Trace Norm Distances for Quantifying Coherence
• The Chernoff lower bound for symmetric quantum hypothesis testing
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Cited by in corpus (8)

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• Probabilistic state synthesis based on optimal convex approximation
• The optimal approximation of qubit states with limited quantum states
• Comment on "Optimal convex approximations of quantum states"
• Probabilistic unitary synthesis with optimal accuracy
• The best approximation of an objective state with a given set of quantum states
• The best approximation of a given qubit state with the limited pure-state set