# Relations between bipartite entanglement measures

## TL;DR

This paper explores the relationships between source and accessible entanglement measures for bipartite pure states, providing analytical characterizations, boundaries, and comparisons with other entanglement measures.

## Contribution

It introduces an analytical method using the Positivstellensatz to determine accessible and source regimes for bipartite pure states and relates these to other entanglement measures.

## Key findings

- Derived analytical boundaries for entanglement measure regimes
- Established conditions for the physical availability of parameter regimes
- Compared behaviors of different entanglement measures

## Abstract

We investigate the properties and relations of two classes of operational bipartite and multipartite entanglement measures, the so-called source and the accessible entanglement. The former measures how easy it is to generate a given state via local operations and classical communication (LOCC) from some other state, whereas the latter measures the potentiality of a state to be convertible to other states via LOCC. Main emphasis is put on the bipartite pure states, single copy regime. We investigate which parameter regime is physically available, i.e for which values of these measures does there exist a bipartite pure state. Moreover, we determine, given some state, which parameter regime can be accessed by it and from which parameter regime it can be accessed. We show that this regime can be determined analytically using the Postitivstellensatz. Moreover, we compute the boundaries of these sets and the boundaries of the corresponding source and accessible sets. Furthermore, we relate these results to other entanglement measures and compare their behaviors. Apart from that, an operational characterization of bipartite pure state entanglement is presented.