A Family of Monotone Quantum Relative Entropies

Mathieu Lewin; Julien Sabin

doi:10.1007/s11005-014-0689-y

A Family of Monotone Quantum Relative Entropies

Mathieu Lewin
, Julien Sabin

CY Cergy Paris Université

Research output: Contribution to journal › Article › peer-review

Abstract

We study here the elementary properties of the relative entropy H_φ(A, B) = Tr[φ(A) - φ(B) - φ′(B)(A - B)] for φ a convex function and A, B bounded self-adjoint operators. In particular, we prove that this relative entropy is monotone if and only if φ′ is operator monotone. We use this to appropriately define H_φ(A, B) in infinite dimension.

Original language	English
Pages (from-to)	691-705
Number of pages	15
Journal	Letters in Mathematical Physics
Volume	104
Issue number	6
DOIs	https://doi.org/10.1007/s11005-014-0689-y
Publication status	Published - 1 Jan 2014
Externally published	Yes

Keywords

Klein inequality
matrix inequalities
relative entropy
strong subadditivity

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10.1007/s11005-014-0689-y

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N2 - We study here the elementary properties of the relative entropy Hφ(A, B) = Tr[φ(A) - φ(B) - φ′(B)(A - B)] for φ a convex function and A, B bounded self-adjoint operators. In particular, we prove that this relative entropy is monotone if and only if φ′ is operator monotone. We use this to appropriately define Hφ(A, B) in infinite dimension.

AB - We study here the elementary properties of the relative entropy Hφ(A, B) = Tr[φ(A) - φ(B) - φ′(B)(A - B)] for φ a convex function and A, B bounded self-adjoint operators. In particular, we prove that this relative entropy is monotone if and only if φ′ is operator monotone. We use this to appropriately define Hφ(A, B) in infinite dimension.

KW - Klein inequality

KW - matrix inequalities

KW - relative entropy

KW - strong subadditivity

UR - https://www.scopus.com/pages/publications/84900305317

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DO - 10.1007/s11005-014-0689-y

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JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

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ER -

A Family of Monotone Quantum Relative Entropies

Abstract

Keywords

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