Locally maximally entangleable states and W-type states

TL;DR

This paper explores the relationship between locally maximally entangleable states and W-type states, showing that certain three-qubit W-type states are LME, but no W-type states with four or more qubits are LME, impacting state preparation methods.

Contribution

It proves that some three-qubit W-type states are LME, while all W-type states with four or more qubits are not, clarifying their entanglement properties under SLOCC.

Findings

Some three-qubit W-type states are LME.

No W-type states with four or more qubits are LME.

Four-qubit W-type states cannot be prepared using LME states under SLOCC.

Abstract

We investigate the relationship between locally maximally entangleable (LME) states and W-type states which are equivalent to a W state under stochastic local operations and classical communication (SLOCC). We prove that (i) some special W-type states of three qubits are LME; and (ii) no W-type state of four and more qubits is LME. Our results show that the W state of four and more qubits cannot be prepared by using LME states under SLOCC. However, for three qubits some special LME states can be used to prepare the W state under SLOCC.