Discriminating strength: a bona fide measure of non-classical correlations

Abstract

A new measure of non-classical correlations is introduced and characterized. It tests the ability of using a state ρ of a composite system AB as a probe for a quantum illumination task (e.g. see Lloyd 2008 Science http://dx.doi.org/10.1126/science.1160627 321 http://dx.doi.org/10.1126/science.1160627 ), in which one is asked to remotely discriminate between the two following scenarios: (i) either nothing happens to the probe, or (ii) the subsystem A is transformed via a local unitary ${{R}_{A}}$ whose properties are partially unspecified when producing ρ . This new measure can be seen as the discrete version of the recently introduced interferometric power measure (Girolami et al 2013 e-print arXiv: http://arXiv.org/abs/1309.1472 ) and, at least for the case in which A is a qubit, it is shown to coincide (up to an irrelevant scaling factor) with the local quantum uncertainty measure of Girolami, Tufarelli and Adesso (2013 Phys. Rev. Lett. http://dx.doi.org/10.1103/PhysRevLett.110.240402 110 http://dx.doi.org/10.1103/PhysRevLett.110.240402 ). Analytical expressions are derived which allow us to formally prove that, within the set of separable configurations, the maximum value of our non-classicality measure is achieved over the set of quantum-classical states (i.e. states ρ which admit a statistical unravelling where each element of the associated ensemble is distinguishable via local measures on B ).

Keywords

• quantum correlations
• state discrimination
• quantum metrology
• quantum discord
• quantum information