Quantumness of correlations and entanglement

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.

14 pages, no figures, revision version, Accepted for publication in the Special Issue of the International Journal of Quantum Information devoted to "Quantum Correlations: entanglement and beyond"

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• Operational interpretations of quantum discord
• Linking Quantum Discord to Entanglement in a Measurement
• Completely Positive Maps and Classical Correlations
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• Generalized information theoretic measure to discern the quantumness of correlations

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• On the Debate Concerning the Proper Characterisation of Quantum Dynamical Evolution
• Quantum Channel Negativity as a Measure of System-Bath Coupling and Correlation
• On the Necessity of Entanglement for the Explanation of Quantum Speedup
• On the Physical Explanation for Quantum Computational Speedup