On the distinguishability of random quantum states

Details On the distinguishability of random quantum states On the distinguishability of random quantum states

2006-07-03

arxiv.org/abs/quant-ph/0607011v2

Comm. Math. Phys. 273(3), pp. 619-636, 2007

Physics

Quantum Physics

20 pages, 2 figures; v2 fixes typos and an error in an appendix

Scientific paper

10.1007/s00220-007-0221-7

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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