A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy

Eric A. Carlen, Élliott H. Lieb

Anna Vershynina, Eric A. Carlen, Élliott H. Lieb

Eric A. Carlen, Élliott H. Lieb

We consider the following trace function on n-tuples of positive operators: Φ_p(A_1,A_2,...,A_n) = Trace (\sum_{j=1}^n A_j^p)^{1/p} and prove that it is jointly concave for 02, Φ_p is neither convex nor concave. We conjecture that Φ_p is convex for 1

Ting-Chun Lin, Isaac H. Kim, Min-Hsiu Hsieh

Vladimir I. Man’ko, Liubov A. Markovich

The two-parameter Minkowski like inequality written for composite quantum system state is obtained for arbitrary Hermitian non-negative matrix with trace equal to unity. The inequality can be used as entropic and information inequality for density matrix of noncomposite finite quantum system, e.g. for a single qudit state. The analogs of strong subadditivity condition for the single qudit is discussed in context of obtained Minkowski like inequality.

Mary Beth Ruskai