Seven definitions of bipartite bound entanglement

TL;DR

This paper reviews and unifies seven different definitions of bipartite bound entanglement, demonstrating their equivalence and clarifying the structure of bound entangled states in quantum information theory.

Contribution

It provides a comprehensive analysis that unifies and extends previous scattered results, establishing the equivalence of seven definitions of bound entanglement.

Findings

All seven definitions of bipartite bound entanglement are equivalent.

Critical distillation protocols are analyzed to support the equivalence.

The structure of bound entanglement states is clarified and better understood.

Abstract

An entangled state is bound entangled, if one cannot combine any number of copies of the state to a maximally entangled state, by using only local operations and classical communication. If one formalizes this notion of bound entanglement, one arrives immediately at four different definitions. In addition, at least three more definitions are commonly used in the literature, in particular so in the very first paper on bound entanglement. Here we review critical distillation protocols and we examine how different results from quantum information theory interact in order to prove that all seven definitions are eventually equivalent. Our self-contained analysis unifies and extends previous results scattered in the literature and reveals details of the structure of bound entanglement.