A measure of total correlations cannot increase under deterministic local operations. We show that, for any number of systems, this condition alone does not guarantee the existence of maximally correlated states. Namely, there is no state that simultaneously maximizes all the measures satisfying it. If, in addition, the measures do not increase with probability unity under local measurements, then such states exist for two systems. They are the maximally entangled states. For a larger number of systems, it depends on their Hilbert-space dimensions.

• Received 7 August 2018

DOI:https://doi.org/10.1103/PhysRevA.98.052306