The Chernoff lower bound for symmetric quantum hypothesis testing

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dc.creatorNussbaum, Michael
dc.creatorSzkoła, Arleta
dc.date2006-07-30
dc.date2009-04-27
dc.date.accessioned2026-07-07T13:10:04Z
dc.date.available2026-07-07T13:10:04Z
dc.descriptionWe consider symmetric hypothesis testing in quantum statistics, where the hypotheses are density operators on a finite-dimensional complex Hilbert space, representing states of a finite quantum system. We prove a lower bound on the asymptotic rate exponents of Bayesian error probabilities. The bound represents a quantum extension of the Chernoff bound, which gives the best asymptotically achievable error exponent in classical discrimination between two probability measures on a finite set. In our framework, the classical result is reproduced if the two hypothetic density operators commute. Recently, it has been shown elsewhere [Phys. Rev. Lett. 98 (2007) 160504] that the lower bound is achievable also in the generic quantum (noncommutative) case. This implies that our result is one part of the definitive quantum Chernoff bound.
dc.descriptionPublished in at http://dx.doi.org/10.1214/08-AOS593 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/quant-ph/0607216
dc.identifierhttp://arxiv.org/abs/quant-ph/0607216
dc.identifierAnnals of Statistics 2009, Vol. 37, No. 2, 1040-1057
dc.identifierdoi:10.1214/08-AOS593
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/228942
dc.subjectQuantum Physics
dc.subject62P35, 62G10 (Primary)
dc.titleThe Chernoff lower bound for symmetric quantum hypothesis testing
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