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arXiv · 2403.12926

Decoherence-free algebras in quantum dynamics

Daniele Amato·Paolo Facchi·Arturo Konderak
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Abstract

In this Article we analyze the algebraic properties of the asymptotic dynamics of finite-dimensional open quantum systems in the Heisenberg picture. In particular, a natural product (Choi-Effros product) can be defined in the asymptotic regime. Motivated by this structure, we introduce a new space called the Choi-Effros decoherence-free algebra. Interestingly, this space is both a C*-algebra with respect to the composition product, and a B*-algebra with respect to the Choi-Effros product. Moreover, such space admits a direct-sum decomposition revealing a clear relationship with the attractor subspace of the dynamics. In particular, the equality between the attractor subspace and the Choi-Effros decoherence-free algebra is a necessary and sufficient condition for a faithful dynamics. Finally, we show how all the findings do not rely on complete positivity but on the much weaker Schwarz property.

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Daniele Amato, Paolo Facchi, Arturo Konderak. 2024-03-19. Decoherence-free algebras in quantum dynamics. https://doi.org/10.1007/s11005-026-02095-3

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