Ruminations on matrix convexity and the strong subadditivity of quantum entropy

Michael Aizenman; Giorgio Cipolloni

doi:10.1007/s11005-023-01638-2

Ruminations on matrix convexity and the strong subadditivity of quantum entropy

Michael Aizenman
, Giorgio Cipolloni

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

3 Scopus citations

Abstract

The familiar second derivative test for convexity, combined with resolvent calculus, is shown to yield a useful tool for the study of convex matrix-valued functions. We demonstrate the applicability of this approach on a number of theorems in this field. These include convexity principles which play an essential role in the Lieb–Ruskai proof of the strong subadditivity of quantum entropy.

Original language	English (US)
Article number	18
Journal	Letters in Mathematical Physics
Volume	113
Issue number	1
DOIs	https://doi.org/10.1007/s11005-023-01638-2
State	Published - Feb 2023

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Keywords

26B25
47H05
81Q05
82B10
Matrix convexity
Parallel sums
Quantum entropy
Strong subadditivity

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10.1007/s11005-023-01638-2

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abstract = "The familiar second derivative test for convexity, combined with resolvent calculus, is shown to yield a useful tool for the study of convex matrix-valued functions. We demonstrate the applicability of this approach on a number of theorems in this field. These include convexity principles which play an essential role in the Lieb–Ruskai proof of the strong subadditivity of quantum entropy.",

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AB - The familiar second derivative test for convexity, combined with resolvent calculus, is shown to yield a useful tool for the study of convex matrix-valued functions. We demonstrate the applicability of this approach on a number of theorems in this field. These include convexity principles which play an essential role in the Lieb–Ruskai proof of the strong subadditivity of quantum entropy.

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KW - 81Q05

KW - 82B10

KW - Matrix convexity

KW - Parallel sums

KW - Quantum entropy

KW - Strong subadditivity

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Ruminations on matrix convexity and the strong subadditivity of quantum entropy

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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