Entanglement certification from moments of positive maps
Qing-Hua Zhang, Xiaoyu Ma, Shao-Ming Fei

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.
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