Abstract

Entropy inequalities are linear inequalities relating the von Neumann entropies of different overlapping marginals of a quantum state. These inequalities are a mathematical consequence of the postulates of quantum mechanics and are an indispensable tool in quantum information science. All (unconstrained) entropy inequalities we know today follow from the celebrated strong subadditivity of quantum entropy and it is a major open problem to prove an unconstrained entropy inequality that is independent of strong subadditivity. In this talk I will present a novel approach to prove entropy inequalities based on recent developments on trace inequalities. This approach can be used to prove all entropy inequalities we currently know in a unified way. Furthermore, it could be a useful tool in proving the first unconstrained entropy inequality that does not trivially follow from strong subadditivity.