An Exponential Mixing Condition for Quantum Channels
<|reference_start|>An Exponential Mixing Condition for Quantum Channels: 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.<|reference_end|>
@article{souissi2024an,
    title={An Exponential Mixing Condition for Quantum Channels},
    author={Abdessatar Souissi, Abdessatar Barhoumi},
    journal={arXiv preprint arXiv:2407.16031},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.16031},
    primaryClass={quant-ph cs.IT math.IT}
}