Entanglement certification from moments of positive maps

TL;DR

This paper introduces a new entanglement certification method using moments of positive maps, avoiding eigenvalue calculations, and leveraging the Faddeev-LeVerrier algorithm to detect negative eigenvalues.

Contribution

It proposes a novel entanglement criterion based on positive maps and matrix moments, simplifying detection without eigenvalue computation.

Findings

Effective in certifying entanglement with partial state knowledge

Utilizes Faddeev-LeVerrier algorithm to relate polynomial coefficients to eigenvalues

Relies on selecting appropriate positive maps for optimal results

Abstract

Entanglement certification is crucial in physical experiments, particularly when only partial knowledge of the quantum state is available. In this context, we present an entanglement criterion based on positive but not completely positive maps, which eliminates the need to identify eigenvalues of the output state. Notably, the Faddeev-LeVerrier algorithm establishes a relationship between the coefficients of characteristic polynomials and the moments of a matrix. This enables the existence of negative eigenvalues through the moments of the output state. The effectiveness of our criterion relies on the selection of positive maps, similar to the original positive maps criterion.