A simplex of bound entangled multipartite qubit states

Abstract

We construct a simplex for multipartite qubit states of even number n of qubits, which has the same geometry concerning separability, mixedness, kind of entanglement, amount of entanglement and nonlocality as the bipartite qubit states. We derive the entanglement of the class of states which can be described by only three real parameters with the help of a multipartite measure for all discrete systems. We prove that the bounds on this measure are optimal for the whole class of states and that it reveals that the states possess only n-partite entanglement and not e.g. bipartite entanglement. We then show that this n-partite entanglement can be increased by stochastic local operations and classical communication to the purest maximal entangled states. However, pure n-partite entanglement cannot be distilled, consequently all entangled states in the simplex are n-partite bound entangled. We study also Bell inequalities and find the same geometry as for bipartite qubits. Moreover, we show how the (hidden) nonlocality for all n-partite bound entangled states can be revealed.

11 pages, 4 figures; 2nd version changed considerably and a detailed derivation of the multipartite measure is included

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• Multipartite entanglement measures
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• A composite parameterization of unitary groups, density matrices and subspaces
• Free versus Bound Entanglement: Machine learning tackling a NP-hard problem
• Two computable sets of multipartite entanglement measures
• Accessible quantification of multiparticle entanglement
• Characterizing entanglement with geometric entanglement witnesses
• Mutually Unbiased Bases and Bound Entanglement
• Geometry of two-body correlations in three-qubit states
• Mixed State Entanglement Measures for Intermediate Separability