Approximation of multipartite quantum states: revised version with new applications

• URL: http://arxiv.org/abs/2401.02388v1
• Date: Thu, 4 Jan 2024 17:59:01 GMT
• Title: Approximation of multipartite quantum states: revised version with new applications
• Authors: M.E.Shirokov
• Abstract summary: We show that for any multipartite state with finite energy the infimum in the definition of the relative entropy of $pi$-entanglement can be taken over the set of finitely-decomposable $pi$-separable states with finite energy. We also show that for any multipartite state with finite energy the infimum in the definition of the relative entropy of $pi$-entanglement can be taken over the set of finitely-decomposable $pi$-separable states with finite energy.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Special approximation technique for analysis of different characteristics of states of multipartite infinite-dimensional quantum systems is proposed and applied to the study of the relative entropy of $\pi$-entanglement and its regularisation. In particular, by using this technique we obtain simple sufficient conditions for local continuity (convergence) of the regularized relative entropy of $\pi$-entanglement. We establish a finite-dimensional approximation property for the relative entropy of entanglement and its regularization that allows us to generalize to the infinite-dimensional case the results proved in the finite-dimensional settings. We also show that for any multipartite state with finite energy the infimum in the definition of the relative entropy of $\pi$-entanglement can be taken over the set of finitely-decomposable $\pi$-separable states with finite energy.

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