The source and accessible entanglement of few-body systems

TL;DR

This paper introduces explicit formulas and computational methods for source and accessible entanglement measures in multipartite quantum systems, enhancing understanding of state transformations under LOCC.

Contribution

It derives explicit formulas for source entanglement and provides numerical methods for accessible entanglement, including conditions for LOCC transformations in four-qubit states.

Findings

Explicit formulas for source entanglement in bipartite and multipartite states

Numerical computation methods for accessible entanglement

Necessary and sufficient conditions for LOCC transformations among four-qubit states

Abstract

Entanglement is the resource to overcome the natural limitations of spatially separated parties restricted to Local Operations assisted by Classical Communications (LOCC). Recently two new classes of operational entanglement measures, the source and the accessible entanglement, for arbitrary multipartite states have been introduced. Whereas the source entanglement measures from how many states the state of interest can be obtained via LOCC, the accessible entanglement measures how many states can be reached via LOCC from the state at hand. We consider here pure bipartite as well as multipartite states and derive explicit formulae for the source entanglement. Moreover, we obtain explicit formulae for a whole class of source entanglement measures that characterize the simplicity of generating a given bipartite pure state via LOCC. Furthermore, we show how the accessible entanglement can be computed numerically. For generic four-qubit states we first derive the necessary and sufficient conditions for the existence of LOCC transformations among these states and then derive explicit formulae for their accessible and source entanglement.