The minimal entanglement of bipartite decompositions as a witness of strong entanglement in a quantum system

TL;DR

This paper introduces the minimal entanglement of bipartite decompositions (MEBD) as a new measure to characterize strong multipartite entanglement in quantum systems, with practical estimation methods and examples in spin chains.

Contribution

The paper defines MEBD as a novel measure for multipartite entanglement and provides a lower estimation method along with examples in spin-1/2 chains.

Findings

MEBD vanishes for systems decomposable into weakly entangled parts

Large MEBD indicates strongly entangled systems unsuitable for simple bipartite decomposition

Examples demonstrate big MEBD in spin chains under specific Hamiltonian conditions

Abstract

We {characterize the multipartite entanglement in a quantum system by the quantity} which vanishes if only the quantum system may be decomposed into two weakly entangled subsystems, unlike measures of multipartite entanglement introduced before. We refer to this {quantity} as the minimal entanglement of bipartite decompositions (MEBD). Big MEBD means that the system may not be decomposed into two weakly entangled subsystems. MEBD allows one to define, for instance, whether the given quantum system may be a candidate for a quantum register, where the above decomposition is undesirable. A method of lower estimation of MEBD is represented. Examples of big MEBD in spin-1/2 chains governed by the $H_{dz}$ Hamiltonian in the strong external magnetic field are given.