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On the distinguishability of random quantum states

Ashley Montanaro
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Abstract

We develop two analytic lower bounds on the probability of success p of identifying a state picked from a known ensemble of pure states: a bound based on the pairwise inner products of the states, and a bound based on the eigenvalues of their Gram matrix. We use the latter to lower bound the asymptotic distinguishability of ensembles of n random quantum states in d dimensions, where n/d approaches a constant. In particular, for almost all ensembles of n states in n dimensions, p>0.72. An application to distinguishing Boolean functions (the "oracle identification problem") in quantum computation is given.

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Ashley Montanaro. 2006-07-11. On the distinguishability of random quantum states. https://doi.org/10.1007/s00220-007-0221-7

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