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Trapped Ion Quantum Computing

Optimality Condition for the Petz Map

arXiv
Authors: Bikun Li, Zhaoyou Wang, Guo Zheng, Yat Wong, Liang Jiang

Year

2024

Paper ID

37414

Status

Preprint

Abstract Read

~2 min

Abstract Words

104

Citations

N/A

Abstract

In quantum error correction, the Petz map serves as a perfect recovery map when the Knill-Laflamme conditions are satisfied. Notably, while perfect recovery is generally infeasible for most quantum channels of finite dimension, the Petz map remains a versatile tool with near-optimal performance in recovering quantum states. This work introduces and proves, for the first time, the necessary and sufficient conditions for the optimality of the Petz map in terms of entanglement fidelity. In some special cases, the violation of this condition can be easily characterized by a simple commutator that can be efficiently computed. We provide multiple examples that substantiate our new findings.

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.
  • In quantum error correction, the Petz map serves as a perfect recovery map when the Knill-Laflamme conditions are satisfied.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2410.23622 [2] arXiv https://arxiv.org/abs/2410.23622 [3] Publisher https://arxiv.org/abs/2410.23622

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