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

References in corpus (8)

• The state space for two qutrits has a phase space structure in its core
• The geometry of bipartite qutrits including bound entanglement
• Geometric entanglement witnesses and bound entanglement
• Bound entanglement in the magic simplex of two--qutrits
• Multipartite entanglement measure for all discrete systems
• Entanglement of a class of mixed two - qutrit states
• Extending Bell inequalities to more parties
• Bloch vectors for qudits and geometry of entanglement

Cited by in corpus (2)

• Two computable sets of multipartite entanglement measures
• Characterizing entanglement with geometric entanglement witnesses