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Journal Articles Quantum Information Processing Year : 2024

k-Positivity and Schmidt number under orthogonal group symmetries

Abstract

In this paper, we present a new application of group theory to develop a systematical approach to efficiently compute the Schmidt numbers. The Schmidt number is a natural quantification of entanglement in quantum information theory, but computing its exact value is generally a challenging task even for very concrete examples. We exhibit a complete characterization of all orthogonally covariant k-positive maps. This result generalizes earlier results by Tomiyama (Linear Algebra Appl 69:169–177, 1985). Furthermore, we optimize duality relations between k-positivity and Schmidt numbers under group symmetries. This new approach enables us to transfer the results of k-positivity to the computation of the Schmidt numbers of all orthogonally invariant quantum states.

Dates and versions

hal-04608989 , version 1 (12-06-2024)

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Sang-Jun Park, Sang-Gyun Youn. k-Positivity and Schmidt number under orthogonal group symmetries. Quantum Information Processing, 2024, 23, pp.162. ⟨10.1007/s11128-024-04361-6⟩. ⟨hal-04608989⟩
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