Entanglement Monogamy of Tripartite Quantum States

TL;DR

This paper discovers a Pythagorean-like monogamy relation among bipartite and tripartite entanglement measures in tripartite quantum states, introducing a new entanglement monotone and extending results to mixed and multipartite states.

Contribution

It introduces a novel monogamy equation resembling the Pythagorean theorem for tripartite entanglement and defines a new genuine tripartite entanglement monotone.

Findings

Derived a Pythagorean-like monogamy relation for pure states.

Established a new genuine tripartite entanglement monotone.

Extended results to mixed and multipartite quantum states.

Abstract

An interesting monogamy equation with the form of Pythagorean theorem is found for $2\otimes 2\otimes n$-dimensional pure states, which reveals the relation among bipartite concurrence, concurrence of assistance, and genuine tripartite entanglement. At the same time, a genuine tripartite entanglement monotone as a generalization of 3-tangle is naturally obtained for $(2\otimes 2\otimes n)$- dimensional pure states in terms of a distinct idea. For mixed states, the monogamy equation is reduced to a monogamy inequality. Both results for tripartite quantum states can be employed to multipartite quantum states.