Communications in Mathematical Physics

, Volume 273, Issue 3, pp 619–636 | Cite as

On the Distinguishability of Random Quantum States

  • Ashley MontanaroEmail author


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.


Quantum State Boolean Function Pure State Random Matrix Theory Hypergeometric Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of BristolBristolUK

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