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

Sang-Jun Park; Sang-Gyun Youn

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arXiv · 2306.00654

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

Sang-Jun Park·Sang-Gyun Youn

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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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Sang-Jun Park, Sang-Gyun Youn. 2023-06-01. $k$-positivity and Schmidt number under orthogonal group symmetries. https://arxiv.org/abs/2306.00654

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