From joint convexity of quantum relative entropy to a concavity theorem of Lieb

Remarks on two theorems of E. Lieb

H. Epstein · 1973

Earlier work this paper cites.

Convex trace functions and the Wigner–Yanase–Dyson conjecture

E. H. Lieb · 1973

Earlier work this paper cites.

Expectations and entropy inequalities for finite quantum systems

G. Lindblad · 1974

Earlier work this paper cites.

Relative entropy and the Wigner–Yanase–Dyson–Lieb concavity in an interpolation theory

A. Uhlmann · 1977

Earlier work this paper cites.

Form convex functions and the WYDL and other inequalities

W. Pusz and S. L. Woronowicz · 1978

Earlier work this paper cites.

Concavity of certain maps on positive definite matrices and applications to Hadamard products

T. Ando · 1979

Cited alongside, same era.

A survey of certain trace inequalities

D. Petz · 1994

Cited alongside, same era.

Matrix Analysis

R. Bhatia · 1997

Cited alongside, same era.

Inequalities for quantum entropy: A review with conditions for equality

M. B. Ruskai · 2002

Cited alongside, same era.

Erratum: Inequalities for quantum entropy: A review with conditions for equality [ J. Math. Phys. 43, 4358 (2002)]

M. B. Ruskai · 2005

Cited alongside, same era.

Extensions of Lieb’s concavity theorem

F. Hansen · 2006

Later among the works it cites.

Matrix nearness problems with Bregman divergences

I. S. Dhillon and J. A. Tropp · 2007

Later among the works it cites.

A Minkowski-type trace inequality and strong subadditivity of quantum entropy II: Convexity and concavity

E. A. Carlen and E. H. Lieb · 2008

Later among the works it cites.

A matrix convexity approach to some celebrated quantum inequalities

E. G. Effros · 2009

Later among the works it cites.

User-friendly tail bounds for sums of random matrices

J. A. Tropp · 2010

Later among the works it cites.