Two computable sets of multipartite entanglement measures

TL;DR

This paper introduces two new sets of computable measures for multipartite qudit entanglement, distinguishing separability types and entanglement 'kinds', with explicit bounds often matching PPT criteria.

Contribution

It extends the concept of k-separability to a novel b3_k-separability and provides explicit bounds for these measures in multipartite qudit systems.

Findings

Lower bounds can be derived from entropy and m-concurrences.

Bounds are often tight or match PPT criteria.

New separability concept b3_k-separability introduced.

Abstract

We present two sets of computable entanglement measures for multipartite systems where each subsystem can have different degrees of freedom (so-called qudits). One set, called 'separability' measure, reveals which of the subsystems are separable/entangled. For that we have to extend the concept of k-separability for multipartite systems to a novel unambiguous separability concept which we call \gamma_k-separability. The second set of entanglement measures reveals the 'kind' of entanglement, i.e. if it is bipartite, tripartite, ..., n-partite entangled and is denoted as the 'physical' measure. We show how lower bounds on both sets of measures can be obtained by the observation that any entropy may be rewritten via operational expressions known as m-concurrences. Moreover, for different classes of bipartite or multipartite qudit systems we compute the bounds explicitly and discover that they are often tight or equivalent to positive partial transposition (PPT).