Detecting bipartite entanglement with PnCP maps and non-negative polynomials

Fuente: arXiv
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Main Authors: Massé, Gaël, Rezig, Mounir, Catala, Paul, Scheiner, Santiago, Córdoba, Laia Serradesanferm, Oudot, Enky, Markham, Damian
Format: Preprint
Published: 2026
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author Massé, Gaël
Rezig, Mounir
Catala, Paul
Scheiner, Santiago
Córdoba, Laia Serradesanferm
Oudot, Enky
Markham, Damian
author_facet Massé, Gaël
Rezig, Mounir
Catala, Paul
Scheiner, Santiago
Córdoba, Laia Serradesanferm
Oudot, Enky
Markham, Damian
contents Positive non-Completely Positive (PnCP) maps are an essential tool to detect entanglement since their characterization is a dual aspect of the separability problem. A recent algorithm proposed by Kelp et al. explains how to generate PnCP maps based on the construction of certain positive non-Sum-of-Squares polynomials. We implement this algorithm in a numerically robust way and propose a working version on GitHub. We theoretically demonstrate that the maps produced by the algorithm are indecomposable, localized on the boundary of the positive cone and show that they are inequivalent with most other known PnCP maps. We numerically investigate their entanglement power, demonstrating notably that they are capable of detecting PPT entangled states that most criteria fail to detect.
format Preprint
id arxiv_https___arxiv_org_abs_2605_30426
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Detecting bipartite entanglement with PnCP maps and non-negative polynomials
Massé, Gaël
Rezig, Mounir
Catala, Paul
Scheiner, Santiago
Córdoba, Laia Serradesanferm
Oudot, Enky
Markham, Damian
Quantum Physics
Positive non-Completely Positive (PnCP) maps are an essential tool to detect entanglement since their characterization is a dual aspect of the separability problem. A recent algorithm proposed by Kelp et al. explains how to generate PnCP maps based on the construction of certain positive non-Sum-of-Squares polynomials. We implement this algorithm in a numerically robust way and propose a working version on GitHub. We theoretically demonstrate that the maps produced by the algorithm are indecomposable, localized on the boundary of the positive cone and show that they are inequivalent with most other known PnCP maps. We numerically investigate their entanglement power, demonstrating notably that they are capable of detecting PPT entangled states that most criteria fail to detect.
title Detecting bipartite entanglement with PnCP maps and non-negative polynomials
topic Quantum Physics
url https://arxiv.org/abs/2605.30426