Maximal entanglement of two delocalized spin-$\frac{1}{2}$ particles

Markus Johansson

Published 2015-09-07Version 1

We describe the entanglement of two delocalized spin-$\frac{1}{2}$ particles in the simplest spatial configuration of three spatial modes with at most one particle per mode. It is show that this is the only number of modes for which maximally entangled states exist in such a system. The set of entangled states, including the set of maximally entangled states, is described and different types of entanglement in terms of Bell-nonlocal correlations for different partitions of the system are identified. In particular we focus on the entangled states that are Bell-local for a tri-partition of the system and cannot be described as a superposition of bi-partite entangled pairs of localized particles. Two entanglement monotones are constructed and it is shown that all other monotones are functions of these. Furthermore, the system has a generic non-trivial local unitary symmetry with a corresponding $2\pi/3$ fractional topological phase.