• gaussian states
• non-classical correlations
• quantum discord
• quantum information

The presence of correlations which do not have a classical counterpart, shared among the subparts of a given system, is one of the best signatures of non-classicality for a quantum state. Although entanglement is the most remarkable among these correlations, even some separable (i.e. not entangled) mixed states can exhibit non-classical behaviours. After reviewing Quantum Discord, that has been the first correlation measure historically introduced, several other known quantifiers are presented.

Particular attention is dedicated to the geometric measure known as Trace Distance
Discord, that in this thesis has been evaluated in a new class of two-qubit states and
whose maximum value on the set of separable states has been found when the tested subsystem is a qubit and the other one is infinite-dimensional.

Starting from this scenario, a new measure of correlations is then introduced and characterized. It has a clear operational interpretation in the context of state discrimination: it quantifies the ability of a bipartite state to distinguish between the application or not of an unknown local unitary map acting on one subsystem, labelled with A. The dependence upon the spectrum of such unitary map is discussed, showing in particular that the harmonic choice is optimal at least for pure states with dA = 3 and whichever dB (here dA and dB being the dimensions of the two subsystems). It is proven that for a two dimensional subsystem A the maximum over the set of separable states is reached by classical-quantum ones: its value has been computed analytically when dB >= 3 and numerically when dB = 2.

A comparison among all the discussed measures is performed, plotting their value as a function of the parameter of the amplitude damping channel applied to the first subsystem. The result confirms how an appropriate local operation on the tested subsystem can enhance the amount of non-classical correlations.

Eventually, a possible generalization of the new measure to the set of bosonic Gaussian states for continuous variable systems is discussed, evaluating at last the proposed expression on two-mode squeezed thermal states.