A class of entanglement witnesses and a realignment-like criterion

2023/08/14 by Vahid Jannesary, Jannesary, Vahid, Vahid Karimipour +2 · 2 citations
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2308.07019

openalex publication_date 2023/08/14 · openalex created_date 2023/08/16 · openalex updated_date 2026/07/28

Abstract

We present a multi-parameter family of positive maps between spaces of differing dimensions. This framework facilitates the construction of Entanglement Witnesses (EWs) specifically designed for systems living in d₁ × d₂ dimensions. A sufficient condition for positivity is presented. Interestingly, it is shown that all EWs constructed this way are equivalent to a single realignment-like criterion which for d₁ ≠ d₂ is in general stronger than the original realignment criterion. We illustrate effectiveness of this criterion considering examples of Positive Partial Transpose (PPT) entangled states in 3 × 3 and 3 × 4 dimensions.

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• Effective criteria for entanglement witnesses in small dimensions
• A study on Heisenberg-Weyl linear maps

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