THE CHERNOFF LOWER BOUND FOR SYMMETRIC QUANTUM HYPOTHESIS TESTING

By Michael Nussbaum, Arleta Szkola. 2006

217 citations recorded by the source corpus.

We 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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6e387d19f39cbd3143aee30e726f08f7cbf43c48

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

In Mathematical Physics

Yazhen Wang

Citations in the corpus

Quantum Computation and Quantum Information (2012, methodology): “For details see Artiles, Gill and Gut¸˘a (2005), Barndorﬀ-Nielsen, Gill and Jupp (2003), Butucea, Gut¸˘a and Artiles ( 2007) and Nussbaum and Szko la (2009).”