Work

Effective criteria for entanglement witnesses in small dimensions

Year: 2025

Type: article

Abstract: We present an effective set of necessary and sufficient criteria for block-positivity of matrices of order 4 over C . The approach is based on Sturm sequences and quartic polynomial positivity conditions presented in recent literature. The procedure allows us to test whether a given 4 × 4 complex matrix corresponds to an entanglement witness, and it is exact when the matrix coefficients belong to the rationals, extended by i . The method can be generalized to H 2 ⊗ H d systems for d > 2 to provide necessary but not sufficient criterion for block-positivity. We also outline an alternative approach to the problem relying on Gröbner bases.

Source: Journal of Physics A Mathematical and Theoretical

DOI: 10.1088/1751-8121/ae0c49

Authors: Łukasz Grzelka, Łukasz Skowronek, Karol Życzkowski

Institutions: Jagiellonian University, Center for Theoretical Physics, Polish Academy of Sciences

Language: English

Topic: Quantum Information and Cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,325

Funder: Narodowe Centrum Nauki