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2019

Pretty simple bounds on quantum state discrimination

Montanaro, Ashley

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We show that the quantum measurement known as the pretty good measurement can be used to identify an unknown quantum state picked from any set of $n$ mixed states that have pairwise fidelities upper-bounded by a constant below 1, given $O(\log n)$ copies of the unknown state, with high success probability in the worst case.

If the unknown state is promised to be pure, there is an explicit measurement strategy which solves this worst-case quantum state discrimination problem with $\widetilde{O}(\|G\|)$ copies, where $G$ is the Gram matrix of the states.

Pretty simple bounds on quantum state discrimination · Around

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Quantum state discrimination
Original
S. Barnett and S. Croke · 1970
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Optimal multiple quantum statistical hypothesis testing
V. P. Belavkin · 1975
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On asymptotically optimal hypothesis testing in quantum statistics
A. S. Holevo · 1979
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On the limit of the largest eigenvalue of the large dimensional sample covariance matrix
Y. Yin, Z. Bai, and P. Krishnaiah · 1988
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A “pretty good” measurement for distinguishing quantum states
P. Hausladen and W. Wootters · 1994
Earlier work this paper cites.

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