Monogamy and entanglement in tripartite quantum states

TL;DR

This paper introduces a monogamy equation for tripartite quantum states that unifies GHZ and W entanglement types and reveals how the difference between concurrence and negativity characterizes W-type entanglement.

Contribution

It presents a novel monogamy relation for tripartite states and links the difference of two entanglement measures to W-type entanglement.

Findings

A monogamy equation for tripartite entanglement is established.

The difference between concurrence and negativity characterizes W-type entanglement.

The relation applies to pure states with two-qubit reduced density matrices.

Abstract

We present an interesting monogamy equation for $(2 \otimes 2 \otimes n)$-dimensional pure states, by which a quantity is found to characterize the tripartite entanglement with the GHZ type and W typeentanglements as a whole. In particular, we, for the first time, reveals that for any quantum state of a pair of qubits, the difference between the two remarkable entanglement measures, concurrence and negativity, characterizes the W type entanglement of tripartite pure states with the two-qubit state as reduced density.