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Asymptotics of quantum relative entropy from a representation theoretical viewpoint

Masahito Hayashi

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In this paper it is proved that the quantum relative entropy D(ρ||σ) can be asymptotically attained by the relative entropy of probabilities given by a certain sequence of positive-operator-valued measures (POVMs). The sequence of POVMs depends on σ, but is independent of the choice of ρ.


PACS

03.65.Fd Algebraic methods

03.65.Ta Foundations of quantum mechanics; measurement theory

02.30.Tb Operator theory

02.20.-a Group theory

MSC

81P15 Quantum measurement theory

47B65 Positive operators and order-bounded operators

81Rxx Groups and algebras in quantum theory

Subjects

Mathematical physics

Quantum information and quantum mechanics

Dates

Issue 16 (27 April 2001)

Received 23 December 2000



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