$k$-positivity and Schmidt number under orthogonal group symmetries

• URL: http://arxiv.org/abs/2306.00654v2
• Date: Thu, 20 Jul 2023 09:20:25 GMT
• Title: $k$-positivity and Schmidt number under orthogonal group symmetries
• Authors: Sang-Jun Park, Sang-Gyun Youn
• Abstract summary: We study $k$-positivity and Schmidt number under standard group symmetries. The Schmidt number is a natural quantification of entanglement in quantum information theory.
• Score: 1.8376637012033794
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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