Polygamy of Distributed Entanglement

TL;DR

This paper reveals that while entanglement itself is monogamous, the potential for entanglement, or distributed entanglement, exhibits polygamous properties, supported by new inequalities and correlation trade-offs in quantum systems.

Contribution

It introduces the concept of one-way unlocalizable entanglement and establishes polygamy inequalities for distributed entanglement in various quantum systems.

Findings

Distributed entanglement is inherently polygamous.

Established polygamy inequality for tripartite systems.

Derived trade-offs between unlocalizable entanglement and other correlations.

Abstract

While quantum entanglement is known to be monogamous (i.e. shared entanglement is restricted in multi-partite settings), here we show that distributed entanglement (or the potential for entanglement) is by nature polygamous. By establishing the concept of one-way unlocalizable entanglement (UE) and investigating its properties, we provide a polygamy inequality of distributed entanglement in tripartite quantum systems of arbitrary dimension. We also provide a polygamy inequality in multi-qubit systems, and several trade offs between UE and other correlation measures.