Decoherence-free algebras in quantum dynamics

• URL: http://arxiv.org/abs/2403.12926v1
• Date: Tue, 19 Mar 2024 17:29:13 GMT
• Title: Decoherence-free algebras in quantum dynamics
• Authors: Daniele Amato, Paolo Facchi, Arturo Konderak,
• Abstract summary: We analyze the dynamics of finite-dimensional open quantum systems in the Heisenberg picture. Motivated by this structure, we introduce a new space called the Choi-Effros decoherence-free algebra. The equality between the attractor subspace and the Choi-Effros decoherence-free algebra is a necessary and sufficient condition for a faithful dynamics.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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