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arXiv:2604.17900

Bound entanglement detection in $4 \otimes 4$ systems via generalized Choi maps

Mazhar Ali

quant-phSubmitted Apr 20, 2026• Announced Apr 21, 2026• 0 citations
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Abstract

We construct a family of positive but not completely positive linear maps acting on four dimensional space. We employ these maps to detect bound entanglement in high dimensional quantum systems.

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A family of linear positive maps in the algebra of 3×33 \times 33×3 complex matrices proposed recently in Bera et al. arXiv:2212.03807 is further analyzed. It provides a generalization of a seminal Choi nondecomposable extremal map in M3M_3M3​. We investigate when generalized Choi maps are optimal, i.e. cannot be represented as a sum of positive and completely positive maps. This property is weaker than extremality, however, it turns out that it plays a key role in detecting quantum entanglement.
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This paper investigates the properties of Choi polynomials and their fundamental role in the theory of positive linear maps between matrix algebras. By focusing on Hermitian symmetric biquadratic forms, we establish a connection between the positivity of these forms and the structure of positive maps. We specifically explore the construction of indecomposable positive maps in matrix algebras, and their application as entanglement witnesses. Our analysis extends to the detection of Positive Partial Transpose (PPT) entangled states and the classification of edge PPT states in Mm(C)⊗Mn(C)M_m(\mathbb{C}) \otimes M_n(\mathbb{C})Mm​(C)⊗Mn​(C). Our results provide a refined framework for identifying non-separable states that escape the standard PPT criterion, contributing to the broader understanding of entanglement distillation and quantum information theory.
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