An explicit pretty-good-measurement protocol solves worst-case quantum state discrimination with O(log n) copies for low-fidelity mixed states and with a Gram-matrix-dependent copy count for pure states.
Minimax quantum state discrimination
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abstract
We derive the optimal measurement for quantum state discrimination without a priori probabilities, i.e. in a minimax strategy instead of the usually considered Bayesian one. We consider both minimal-error and unambiguous discrimination problems, and provide the relation between the optimal measurements according to the two schemes. We show that there are instances in which the minimum risk cannot be achieved by an orthogonal measurement, and this is a common feature of the minimax estimation strategy.
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quant-ph 1years
2019 1verdicts
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Pretty simple bounds on quantum state discrimination
An explicit pretty-good-measurement protocol solves worst-case quantum state discrimination with O(log n) copies for low-fidelity mixed states and with a Gram-matrix-dependent copy count for pure states.