Relationship among locally maximally entanglable states, W states and hypergraph states under local unitary transformations

TL;DR

This paper explores the relationships between hypergraph states, W states, and locally maximally entanglable states, revealing their distinctions and invariances under local unitary transformations, and introduces a method for encoding weighted hypergraphs into LME states.

Contribution

It characterizes the local entanglability of hypergraph and W states, showing hypergraph states are LME but not equivalent to W states, and proposes encoding weighted hypergraphs into LME states.

Findings

All hypergraph states are LME.

Hypergraph states and LME states are not equivalent under local unitaries.

W states are not LME and cannot be converted into hypergraph states via local unitaries.

Abstract

Kruszynska and Kraus [Phys. Rev. A 79, 052304 (2009)] have recently introduced the so-called locally maximally entanglable (LME) states of n qubits which can be maximally entangled to local auxiliary qubits using controlled operations. We characterize the local entanglability of hypergraph states and W states using an approach in [Phys. Rev. A 79, 052304 (2009)]. We show that (i) all hypergraph states are LME; (ii) hypergraph states and LME states are not equivalent under local unitaries; (iii) a W state of n qubits is not LME; and (iv) no hypergraph state of n qubits can be converted into to the W state under local unitary transformations. Moreover, we also present an approach for encoding weighted hypergraphs into LME states.