Convex trace functions and the Wigner-Yanase-Dyson conjecture

By Elliott H. Lieb. 1973

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User-Friendly Tail Bounds for Sums of Random Matrices (2010, background): “This paper demonstrates that a large class of matrix probability inequalities follows from a deep theorem [ 29, Theorem 6 ] of Lieb that appears in his seminal work on convex trace functions.”
Time-uniform Chernoff bounds via nonnegative supermartingales (2018, background): “Fact 3 (Lieb, 1973; Tropp, 2012).”
Introduction to Matrix Analysis and Applications (2014, background): “The joint concavity in (D1, D2) is the famous Lieb’s concavity theorem [58].”
FREEDMAN'S INEQUALITY FOR MATRIX MARTINGALES (2011, unknown): “Theorem 1.4 (Lieb, 1973).”
Modular Hamiltonians on the null plane and the Markov property of the vacuum state (2017, methodology): “5) Following [42] we use the Golden–Thomson–Lieb inequality [44]”
On Some Extensions of Bernstein's Inequality for Self-adjoint Operators (2011, background): “(2d) _Ulog nU2 ˙2 log(2d) : Improvement can be signicant whenever Intdim ˝d. Proof of Theorem2.1. Proof of (2.1) follows the lines of [14], where the key role is played by Lieb’s concavity theorem [7]: Theorem 2.3 (Lieb). Given a xed self-adjoint matrix H, the function A7!trexp(H+ logA) is concave ”
An Introduction to Matrix Concentration Inequalities (2015, unknown): “Matrix concentration 4-20 Lieb’s Theorem Elliott Lieb Theorem 4.5 (Lieb ’73) Fix a symmetric matrix H.”
Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory (2005, background): “Result xxi) is the Lieb concavity theorem [372].”
Inequalities for quantum entropy: A review with conditions for equality (2002, background): “Lieb’s proof [25] of the concavity of the WYD function (8) and his realization of a connection between SSA and Bauman’s concavity conjecture was a crucial breakthrough.”
Notes on Some Entanglement Properties of Quantum Field Theory (2018, methodology): “(3.35) In nonrelativistic quantum mechanics, a version of monotonicity of relative entropy was proved by Lieb and Ruskai [15], along with strong subadditivity of quantum entropy, to which it is closely related.”
Strong converse for identification via quantum channels (2000, background): “(D) Note however that the mapping A 7→ Tr expA is monotone and convex: see Lieb [17].”
Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance (2016, result): “The non-commutative convexity result ultimately derives from Lieb’s concavity Theorem [40].”
The Theory of Quantum Information (2018, background): “Lieb’s concavity theorem was proved by Lieb [146] in 1973.”