Measures of quantum correlations in infinite-dimensional systems

Understand

Several important measures of quantum correlations of a state of a finite-dimensional composite system are defined as linear combinations of marginal entropies of this state.

• This paper is devoted to the infinite-dimensional generalizations of such quantities and to the analysis of their properties.
• We introduce the notion of faithful extension of a linear combination of marginal entropies and consider several concrete examples starting with the quantum mutual information and the quantum conditional entropy.
• Then we show that the conditional mutual information can be uniquely defined as a lower semicontinuous function on the set of all states of a tripartite infinite-dimensional system possessing all the basic properties valid in finite dimensions.