Quantumness of correlations and entanglement

TL;DR

This paper explores generalized measurement schemes, including not completely positive maps, to better understand and quantify the quantumness of correlations and entanglement in bipartite quantum states.

Contribution

It introduces the use of not completely positive (NCP) maps in measurement schemes, expanding the framework for analyzing quantum correlations beyond traditional CP maps.

Findings

NCP projective maps provide new insights into quantumness of correlations.

Inclusion of NCP maps resolves the separability-classicality dichotomy.

Extended measurement schemes reveal non-zero quantum discord in certain separable states.

Abstract

Generalized measurement schemes on one part of bipartite states, which would leave the set of all separable states insensitive are explored here to understand quantumness of correlations in a more general perspecitve. This is done by employing linear maps associated with generalized projective measurements. A generalized measurement corresponds to a quantum operation mapping a density matrix to another density matrix, preserving its positivity, hermiticity and traceclass. The Positive Operator Valued Measure (POVM) -- employed earlier in the literature to optimize the measures of classical/quatnum correlations -- correspond to completely positive (CP) maps. The other class, the not completely positive (NCP) maps, are investigated here, in the context of measurements, for the first time. It is shown that that such NCP projective maps provide a new clue to the understanding the quantumness of correlations in a general setting. Especially, the separability-classicality dichotomy gets resolved only when both the classes of projective maps (CP and NCP) are incorporated as optimizing measurements. An explicit example of a separable state -- exhibiting non-zero quantumn discord when possible optimizing measurements are restricted to POVMs -- is re-examined with this extended scheme incorporating NCP projective maps to elucidate the power of this approach.