Supporting functionals and singular boundary geometry of two-qubit entanglement of formation

Abstract:We give a criterion for the existence of a global supporting affine functional for the entanglement of formation at an entangled two-qubit state. It exists if and only if the spin-flip bilinear form is nondegenerate on the support of the state, or equivalently, if the last concurrence root associated with the support is nonzero. In this case the entanglement of formation is locally Lipschitz continuous. In the degenerate case the state has rank two or three, and its projective support is tangent to the product-state quadric. For suitable perturbations outside the support, the entanglement of formation decreases as the square root of the mixing parameter. The leading term is obtained explicitly. This square-root decrease violates the one-sided Lipschitz bound required for a global supporting affine functional.

arXiv:2609.31097 [quant-ph]

(or arXiv:2609.31097v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.31097 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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