Quantum entanglement as an extremal Kirkwood-Dirac nonreality

TL;DR

This paper establishes a quantitative link between quantum entanglement and nonclassical nonreality of Kirkwood-Dirac quasiprobability, introducing entanglement monotones based on nonreality measures, with implications for quantum foundations and information.

Contribution

It introduces new entanglement monotones derived from Kirkwood-Dirac nonreality, providing closed-form expressions and bounds, and explores their estimation via weak measurements.

Findings

Entanglement monotone based on KD nonreality is a Schur-concave function.

For two-qubit systems, the monotone equals the concurrence of formation.

Bounds relate entanglement to uncertainty measures like trace-norm asymmetry.

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.