dorsal/arxiv
View SchemaOn the distinguishability of random quantum states
| Authors | Ashley Montanaro |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0607011 |
| URL | https://arxiv.org/abs/quant-ph/0607011 |
| DOI | 10.1007/s00220-007-0221-7 |
| Journal | Comm. Math. Phys. 273(3), pp. 619-636, 2007 |
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.
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"abstract": "We develop two analytic lower bounds on the probability of success p of\nidentifying a state picked from a known ensemble of pure states: a bound based\non the pairwise inner products of the states, and a bound based on the\neigenvalues of their Gram matrix. We use the latter to lower bound the\nasymptotic distinguishability of ensembles of n random quantum states in d\ndimensions, where n/d approaches a constant. In particular, for almost all\nensembles of n states in n dimensions, p\u003e0.72. An application to distinguishing\nBoolean functions (the \"oracle identification problem\") in quantum computation\nis given.",
"arxiv_id": "quant-ph/0607011",
"authors": [
"Ashley Montanaro"
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"quant-ph"
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"doi": "10.1007/s00220-007-0221-7",
"journal_ref": "Comm. Math. Phys. 273(3), pp. 619-636, 2007",
"title": "On the distinguishability of random quantum states",
"url": "https://arxiv.org/abs/quant-ph/0607011"
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