New Minkowski type inequalities and entropic inequalities for quantum states of qudits

TL;DR

This paper derives Minkowski-like inequalities for quantum states of qudits, providing new entropic bounds applicable to single noncomposite quantum systems and exploring their relation to strong subadditivity.

Contribution

It introduces a novel Minkowski-like inequality for Hermitian nonnegative matrices representing qudit states, extending entropic inequalities to noncomposite systems.

Findings

Derived a Minkowski-like inequality for qudit states

Established entropic bounds for single quantum systems

Discussed analogs of strong subadditivity for qudits

Abstract

The two-parameter Minkowski like inequality written for composite quantum system state is obtained for arbitrary Hermitian nonnegative 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.