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Trapped Ion Quantum Computing

An Exponential Mixing Condition for Quantum Channels

arXiv
Authors: Abdessatar Souissi, Abdessatar Barhoumi

Year

2024

Paper ID

65092

Status

Preprint

Abstract Read

~2 min

Abstract Words

100

Citations

N/A

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.

Why This Paper Matters

  • This paper contributes to the Trapped-Ion Quantum Computing research area in the Quantum Articles archive.
  • It adds a 2024 reference point for readers tracking recent quantum research.
  • Quantum channels, pivotal in information processing, describe transformations within quantum systems and enable secure communication and error correction.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2407.16031 [2] arXiv https://arxiv.org/abs/2407.16031 [3] Publisher https://arxiv.org/abs/2407.16031

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