Monogamy of quantum entanglement

TL;DR

This paper reviews recent theoretical advances in understanding the monogamy property of quantum entanglement, including inequalities, measures, and future research directions.

Contribution

It summarizes and extends the theoretical framework of monogamy inequalities and introduces new definitions for quantifying entanglement sharing restrictions.

Findings

Squashed entanglement and one-way distillable entanglement are monogamous in arbitrary dimensions.

Generalized monogamy inequalities extend traditional bounds.

Dual polygamy inequalities are also considered.

Abstract

Unlike classical correlation, quantum entanglement cannot be freely shared among many parties. This restricted shareability of entanglement among multi-party systems is known as monogamy of entanglement, which is one of the most fundamental properties of entanglement. Here, we summarize recent theoretical progress in the field of monogamy of entanglement. We firstly review the standard CKW-type monogamy inequalities in terms of various entanglement measures. In particular, the squashed entanglement and one-way distillable entanglement are monogamous for arbitrary dimensional systems. We then introduce some generalized version of monogamy inequalities which extend and sharpen the traditional ones. We also consider the dual polygamy inequalities for multi-party systems. Moreover, we present two new definitions to define monogamy of entanglement. Finally, some challenges and future directions for monogamy of entanglement are highlighted.