A simplex of bound entangled multipartite qubit states

TL;DR

This paper constructs a geometric framework for multipartite qubit states, revealing their bound entanglement properties, optimal entanglement measures, and nonlocality features, analogous to bipartite qubit states.

Contribution

It introduces a simplex model for multipartite qubits with even n, characterizes n-partite bound entanglement, and explores nonlocality and Bell inequalities in this context.

Findings

States possess only n-partite entanglement, not bipartite.

Bound entangled states can be made maximally entangled via stochastic local operations.

Bell inequalities and nonlocality are consistent with bipartite qubit geometry.

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.