Optimal sequence of quantum measurements in the sense of Stein's lemma in quantum hypothesis testing

By Masahito Hayashi. 2002

165 citations recorded by the source corpus.

We derive a necessary and sufficient condition for a sequence of quantum measurements to achieve the optimal performance in quantum hypothesis testing. We discuss what quantum measurement we should perform in order to attain the optimal exponent of the second error probability under the condition that the first error probability goes to 0. As an asymptotically optimal measurement, we propose a projection measurement characterized by the irreducible representation theory of the special linear group SL(). Especially, in the spin-1/2 system, it is realized by the simultaneous measurement of the total momentum and a momentum of a specified direction. As a by-product, we obtain another proof of quantum Stein's lemma. In addition, an asymptotically optimal measurement is constructed in the quantum Gaussian case, and it is physically meaningful.

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

View Paper: https://www.semanticscholar.org/paper/06ce314f9df87400615a959a96ac031c5c41a810

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

A Generalization of Quantum Stein’s Lemma (2009, methodology): “[7] we ﬁnd for each λ , σ λ ≤ dim H λ E λ ( σ λ ) , where H λ is the Hilbert space in which σ λ acts on.”