k-positivity and Schmidt number under orthogonal group symmetries

2023/06/01 by Sangjun Park, Park, Sang-Jun, Sang-Gyun Youn +1 · 1 citation
Chemistry · Mathematics · Physics and Astronomy · #43A65 #46N50 #81P45 #Advanced NMR Techniques and Applications #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2306.00654

openalex publication_date 2023/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study k-positivity and Schmidt number under standard orthogonal group symmetries. The Schmidt number is a natural quantification of entanglement in quantum information theory. First of all, we exhibit a complete characterization of all orthogonally covariant k-positive maps. This generalizes earlier results in [Tom85]. Furthermore, we optimize duality relations between k-positivity and Schmidt numbers under compact group symmetries. This new framework enables us to efficiently compute the Schmidt numbers of all orthogonally invariant quantum states.

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