It's known to be impossible to, with 100% accuracy, discriminate between two different quantum states that are not orthogonal. In this paper we look at how accurately you can make this determination when you are given multiple identical copies of one of the two nonorthogonal states. We consider different measurements you can perform, and find that a measurement strategy that performs optimally when the states in question are pure actually performs poorer than a naive “majority vote” scheme when the states have some mixture. We experimentally demonstrate these schemes and derive (and also demonstrate) an adaptive measurement scheme that performs optimally in all conditions, and compare it to the fundamental limit.
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