Genuine multipartite Rains entanglement

TL;DR

This paper introduces the genuine multipartite Rains entanglement (GMRE), a new measure for quantifying genuine multipartite entanglement using semi-definite programming, and explores its properties and bounds.

Contribution

The paper defines GMRE as a computable multipartite entanglement measure, proves its monotonicity, and relates it to GHZ-distillable entanglement, also generalizing it with other entropies.

Findings

GMRE can be computed via semi-definite programming.

GMRE bounds GHZ-distillable entanglement from above.

A generalized version of GMRE incorporating other entropies is developed.

Abstract

We introduce the genuine multipartite Rains entanglement (GMRE) as a measure of genuine multipartite entanglement that can be computed using semi-definite programming. Similar to the Rains relative entropy (its bipartite counterpart), the GMRE is monotone under selective quantum operations that completely preserve the positivity of the partial transpose, implying that it is a multipartite entanglement monotone. As a consequence, we show that the GMRE bounds both the one-shot standard and probabilistic approximate GHZ-distillable entanglement from above. We also develop a generalization of this quantity that incorporates other entropies, including quantum Renyi relative entropies.