An Entanglement Measure from Quantum Optimal Transport

Abstract:We propose a bipartite entanglement measure $E(\rho)$ defined as the minimal order-1 quantum Wasserstein distance from a state to the set of separable states. Owing to the universal data-processing inequality of the Wasserstein metric, the measure satisfies all fundamental axioms within a single geometric framework. A Lipschitz dual formulation yields explicit lower bounds for pure and mixed states, a sharp constant for two-qubit systems, and an expected value for Haar-random pure states. We further establish a quantitative connection to entanglement witnesses: any negative witness expectation value certifies a lower bound on $E$, and the dual variational bound is exactly the maximal violation achievable by a Lipschitz-1 witness. The approach naturally provides subadditivity, trace-distance estimates, and bounds on local observables, while pointing toward large-deviation conjectures. This work furnishes a versatile paradigm at the interface of entanglement theory, optimal transport, and experimental entanglement detection.

arXiv:2606.04969 [quant-ph]

(or arXiv:2606.04969v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2606.04969 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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