Entanglement quantification made simpler through hypothesis testing

Yitian Wang, Qing-yu Cai

Hiroshi Nagaoka, Masahito Hayashi

The information-spectrum analysis made by Han for classical hypothesis testing for simple hypotheses is extended to a unifying framework including both classical and quantum hypothesis testing. The results are also applied to fixed-length source coding when loosening the normalizing condition for probability distributions and for quantum states. We establish general formulas for several quantities relating to the asymptotic optimality of tests/codes in terms of classical and quantum information spectra

Vlatko Vedral, Martin Bodo Plenio, P. L. Knight

Carlen, Eric

Fuyuhiko Tanaka

Recently, there.have lots of work in quantum hypothesis testing that lies in the core of fascinating applications in quantum information theory.They mainly deal with a simple hypothesis because their main concern is the dis- tinguishability of two quantum states.However, in a practical application, composite hypothesis testing is much important as in classical statistics.In the present paper, we focus on the unbiased test in the quantum composite hypothesis testing.We derive necessary and sufficient conditions on exis- tence of a nontrivial unbiased test in the finite-dimensional Hilbert space.As a practical application, we consider the statistical hypothesis testing of entanglements.It is shown that the uniformly most powerful unbiased test is the random guess for the hypothesis testing.It implies that quan- tum fluctuation conflicts with the concept of hypothesis testing in classical statistics.

晓旭 罗