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arXiv:1612.06491 · Communications in Mathematical Physics

Tripartite-to-Bipartite Entanglement Transformation by Stochastic Local Operations and Classical Communication and the Structure of Matrix Spaces

Yinan Li, Youming Qiao, Xin Wang, Runyao Duan

Published Jan 8, 2018• 8 citations
arXivHTMLPDF
DOI
10.1007/s00220-017-3077-5

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Abstract We present a practical classification scheme for the four-partite entangled states under stochastic local operations and classical communication (SLOCC). By transforming a four-partite state into a triple-state set composed of two tripartite states and a bipartite state, the entanglement classification is reduced to the classification of tripartite and bipartite entanglements. This reduction method has the merit of involving only the linear constrains, and meanwhile provides an insight into the entanglement character of the subsystems.
We consider distillation of ebits between a specified pair of subsystems from pure tripartite states by local operations and classical communication. It is known that, allowing an asymptotically vanishing error, the maximal rate is the minimum of the von Neumann entropies of the two corresponding marginals, and under asymptotic stochastic local operations and classical communication the maximal rate is given by a minimization over a one-parameter family of entanglement measures. In this paper, we determine the direct and strong converse error exponents, and the optimal rate for deterministic transformations.