On a quantum entropy power inequality of Audenaert, Datta, and Ozols
We give a short proof of a recent inequality of Audenaert, Datta, and Ozols, and determine cases of equality.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Engineering topics
Lieb, Elliott H.
Publications and source records attributed to Lieb, Elliott H..
Remainder terms for some quantum entropy inequalities
We consider three von Neumann entropy inequalities: subadditivity; Pinsker's inequality for relative entropy; and the monotonicity of relative entropy. For these we state conditions for equality, and we prove some new error bounds away from equality, including an improved version of Pinsker's inequality.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
On an extension problem for density matrices
We investigate the problem of the existence of a density matrix {rho}{sub 123} on a Hilbert space H{sub 1} Circled-Times H{sub 2} Circled-Times H{sub 3} with given partial traces {rho}{sub 12}= Tr{sub 3} {rho}{sub 123} and {rho}{sub 23}= Tr{sub 1} {rho}{sub 123}. While we do not solve this problem completely, we offer partial results in the form of some necessary and some sufficient conditions on {rho}{sub 12} and {rho}{sub 23}. The quantum case differs markedly from the classical (commutative) case, where the obvious necessary compatibility condition suffices, namely, Tr{sub 1} {rho}{sub 12}= Tr{sub 3}{rho}{sub 23}.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗