On the Distinguishability of Random Quantum States
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, 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.
- Publication:
-
Communications in Mathematical Physics
- Pub Date:
- August 2007
- DOI:
- 10.1007/s00220-007-0221-7
- arXiv:
- arXiv:quant-ph/0607011
- Bibcode:
- 2007CMaPh.273..619M
- Keywords:
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- Quantum State;
- Boolean Function;
- Pure State;
- Random Matrix Theory;
- Hypergeometric Series;
- Quantum Physics
- E-Print:
- 20 pages, 2 figures