Аннотация:
Quantum communication protocols which are secure against eavesdropping utilize exponential error bounds for discrimination between probability measures, such as the classical Chernoff bound. This motivates the study of more general testing problems between different possible states of a quantum system, represented by density operators on a complex Hilbert space. A test or detector in this setting combines a quantum measurement, creating a probability space, with a classical statistical test. We consider testing for fixed hypotheses and an increasing number of identical copies of a quantum system, which implies that the error rates tend to zero exponentially and the focus is on the exponent. Recently many classical large deviation type results on hypothesis testing have been generalized to the
quantum setting, such as Stein's lemma, the Sanov theorem, and also the Chernoff and Hoeffding bounds. We present a unified perspective on some of these problems, where it is possible to derive performance benchmarks from classical minimax risk bounds. We also discuss progress on the problem of discrimination between several quantum hypotheses.
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