Quantum entanglement as an extremal Kirkwood-Dirac nonreality
arXiv:2501.04137 · doi:10.1103/PhysRevA.111.012216
Abstract
Understanding the relationship between various different forms of nonclassicality and their resource character is of great importance in quantum foundation and quantum information. Here, we discuss a quantitative link between quantum entanglement and the anomalous or nonclassical nonreal values of Kirkwood-Dirac (KD) quasiprobability, in a bipartite setting. We first construct an entanglement monotone for a pure bipartite state based on the nonreality of the KD quasiprobability defined over a pair of orthonormal bases in which one of them is a product, and optimizations over these bases. It admits a closed expression as a Schur-concave function of the state of the subsystem having a form of nonadditive quantum entropy. We then construct a bipartite entanglement monotone for generic quantum states using the convex roof extension. Its normalized value is upper bounded by the concurrence of formation, and for two-qubit systems, they are equal. We also derive lower and upper bounds in terms of different forms of uncertainty in the subsystem quantified respectively by an extremal trace-norm asymmetry and a nonadditive quantum entropy. The entanglement monotone can be expressed as the minimum total state disturbance due to a nonselective local binary measurement. Finally, we discuss its estimation using weak value measurement and classical optimization, and its connection with strange weak value and quantum contextuality.
33 pages, no figure, accepted for publication in Physical Review A
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