An Exponential Mixing Condition for Quantum Channels

• URL: http://arxiv.org/abs/2407.16031v1
• Date: Mon, 22 Jul 2024 20:18:44 GMT
• Title: An Exponential Mixing Condition for Quantum Channels
• Authors: Abdessatar Souissi, Abdessatar Barhoumi,
• Abstract summary: We prove that if the Markov-Dobrushin constant of a quantum channel exceeds zero, it exhibits exponential mixing behavior. We also analyze ergodicity of a class of mixed-unitary channels associated with finite groups of unitary operators.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum channels, pivotal in information processing, describe transformations within quantum systems and enable secure communication and error correction. Ergodic and mixing properties elucidate their behavior. In this paper, we establish a sufficient condition for mixing based on a quantum Markov-Dobrushin inequality. We prove that if the Markov-Dobrushin constant of a quantum channel exceeds zero, it exhibits exponential mixing behavior. We explore limitations of some quantum channels, demonstrating that unistochastic channels are not mixing. Additionally, we analyze ergodicity of a class of mixed-unitary channels associated with finite groups of unitary operators. Finally, we apply our results to the qubit depolarizing channel.

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