On the distinguishability of random quantum states
arXiv:quant-ph/0607011 · doi:10.1007/s00220-007-0221-7
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.
20 pages, 2 figures; v2 fixes typos and an error in an appendix
References in corpus (2)
Cited by in corpus (4)
- Unbounded violation of tripartite Bell inequalities
- Generic local distinguishability and completely entangled subspaces
- Two-sided estimates of minimum-error distinguishability of mixed quantum states via generalized Holevo-Curlander bounds
- Error rates of Belavkin weighted quantum measurements and a converse to Holevo's asymptotic optimality theorem