An entanglement measure for n-qubits

TL;DR

This paper introduces a new entanglement measure for n-qubits that is invariant under local operations, permutation, and acts as an entanglement monotone, extending previous three-qubit measures.

Contribution

It demonstrates that the residual entanglement for n qubits is a natural, well-behaved measure of entanglement with desirable invariance and monotonicity properties.

Findings

The measure is SL-invariant and LU-invariant.

It is an entanglement monotone.

It vanishes or is multiplicative for product states.

Abstract

Recently, Coffman, Kundu, and Wootters introduced the residual entanglement for three qubits to quantify the three-qubit entanglement in Phys. Rev. A 61, 052306 (2000). In Phys. Rev. A 65, 032304 (2007), we defined the residual entanglement for $n$ qubits, whose values are between 0 and 1. In this paper, we want to show that the residual entanglement for $n$ qubits is a natural measure of entanglement by demonstrating the following properties. (1). It is SL-invariant, especially LU-invariant. (2). It is an entanglement monotone. (3). It is invariant under permutations of the qubits. (4). It vanishes or is multiplicative for product states.