On the distinguishability of random quantum states
Quantum Physics
2009-11-13 v2
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.
Cite
@article{arxiv.quant-ph/0607011,
title = {On the distinguishability of random quantum states},
author = {Ashley Montanaro},
journal= {arXiv preprint arXiv:quant-ph/0607011},
year = {2009}
}
Comments
20 pages, 2 figures; v2 fixes typos and an error in an appendix