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arXiv:1509.02037 · Physical Review A

Maximal entanglement of two delocalized spin- 12 particles

Markus Johansson

Published Feb 23, 2016• 4 citations
arXivHTMLPDF

Abstract

We describe the entanglement of two indistinguishable delocalized spin-$\frac{1}{2}$ particles in the simplest spatial configuration of three spatial modes with the constraint that at most one particle occupy each mode. It is shown 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 tripartition of the system and cannot be described as a superposition of bipartite entangled pairs of localized particles. Two entanglement invariants are constructed and it is shown that all entanglement monotones are functions of these. Furthermore, the system has a generic nontrivial local unitary symmetry with a corresponding $2\ensuremath{\pi}/3$ fractional topological phase. In addition to this a necessary and sufficient condition for the existence of maximally entangled states in systems of arbitrary numbers of delocalized particles with arbitrary spin, where at most one particle can occupy each mode, is derived.

DOI
10.1103/physreva.93.022328

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We characterize and classify the quantum states of a pair of spin-½ particles in terms of the entanglement of the pair. We describe a general strategy for classifying the quantum states of entangled systems, and apply it to the simplest entangled system available - a pair of spin-½ particles. The method is based on local unitary transformations. We give a set of six parameters that describe an arbitrary pure state of a pair of spins, one of which is the entanglement of the pair. We discuss visual representations of the state of this system, and propose a visualization using a Bloch sphere for each subsystem and a disc to record the `shared' information.