An Exponential Mixing Condition for Quantum Channels
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914882450882560 |
|---|---|
| author | Souissi, Abdessatar Barhoumi, Abdessatar |
| author_facet | Souissi, Abdessatar Barhoumi, Abdessatar |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16031 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Exponential Mixing Condition for Quantum Channels Souissi, Abdessatar Barhoumi, Abdessatar Quantum Physics Information Theory 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. |
| title | An Exponential Mixing Condition for Quantum Channels |
| topic | Quantum Physics Information Theory |
| url | https://arxiv.org/abs/2407.16031 |