A remark on the concavity of entropy

Gisela A. Lassner, Gisela A. Lassner

Paulo E. M. F. Mendonça, Reginaldo de Jesus Napolitano, Marcelo A. Marchiolli +2 more

We propose an alternative fidelity measure (namely, a measure of the degree of similarity) between quantum states and benchmark it against a number of properties of the standard Uhlmann-Jozsa fidelity. This measure is a simple function of the linear entropy and the Hilbert-Schmidt inner product between the given states and is thus, in comparison, not as computationally demanding. It also features several remarkable properties such as being jointly concave and satisfying all of Jozsa's axioms. The trade-off, however, is that it is supermultiplicative and does not behave monotonically under quantum operations. In addition, metrics for the space of density matrices are identified and the joint concavity of the Uhlmann-Jozsa fidelity for qubit states is established.

Isaac H. Kim, Mary Beth Ruskai

We give new upper and lower bounds on the concavity of quantum entropy. Comparisons are given with other results in the literature.

Frank Hansen

Alfred Wehrl

Isaac H. Kim, Mary Beth Ruskai

We give new upper and lower bounds on the concavity of quantum entropy. Comparisons are given with other results in the literature.