Quantum correlation entropy

• URL: http://arxiv.org/abs/2005.05408v3
• Date: Mon, 30 Nov 2020 23:22:56 GMT
• Title: Quantum correlation entropy
• Authors: Joseph Schindler, Dominik \v{S}afr\'anek, Anthony Aguirre
• Abstract summary: We study quantum coarse-grained entropy and demonstrate that the gap in entropy between local and global coarse-grainings is a natural generalization of entanglement entropy to mixed states and multipartite systems. This "quantum correlation entropy" $Srm QC$ is additive over independent systems, measures total nonclassical correlations, and reduces to the entanglement entropy for bipartite pure states.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study quantum coarse-grained entropy and demonstrate that the gap in entropy between local and global coarse-grainings is a natural generalization of entanglement entropy to mixed states and multipartite systems. This "quantum correlation entropy" $S^{\rm QC}$ is additive over independent systems, is invariant under local unitary operations, measures total nonclassical correlations (vanishing on states with strictly classical correlation), and reduces to the entanglement entropy for bipartite pure states. It quantifies how well a quantum system can be understood via local measurements, and ties directly to non-equilibrium thermodynamics, including representing a lower bound on the quantum part of thermodynamic entropy production. We discuss two other measures of nonclassical correlation to which this entropy is equivalent, and argue that together they provide a unique thermodynamically distinguished measure.

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