Communications in Mathematical Physics

, Volume 273, Issue 3, pp 619–636

On the Distinguishability of Random Quantum States


DOI: 10.1007/s00220-007-0221-7

Cite this article as:
Montanaro, A. Commun. Math. Phys. (2007) 273: 619. doi: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, and results from random matrix theory, 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.

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of BristolBristolUK