Entanglement of formation and monogamy of multi-party quantum entanglement

TL;DR

This paper establishes a sufficient condition based on entanglement of formation for the monogamy of multi-party quantum entanglement, extending previous results to arbitrary dimensions and providing a general framework.

Contribution

It introduces a new sufficient condition for monogamy of quantum entanglement using entanglement of formation applicable to multi-party systems of any dimension.

Findings

Additivity of mutual information guarantees monogamy in three-party pure states.

The results are generalized to multi-party systems of arbitrary dimensions.

Illustrative examples demonstrate the applicability of the theoretical conditions.

Abstract

We provide a sufficient condition for the monogamy inequality of multi-party quantum entanglement of arbitrary dimensions in terms of entanglement of formation. Based on the classical-classical-quantum(ccq) states whose quantum parts are obtained from the two-party reduced density matrices of a three-party quantum state, we show the additivity of the mutual information of the ccq states guarantees the monogamy inequality of the three-party pure state in terms of EoF. After illustrating the result with some examples, we generalize our result of three-party systems into any multi-party systems of arbitrary dimensions.