Optimality Condition for the Petz Map
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.
Authors
- Bikun Li (ORCID: https://orcid.org/0000-0001-5044-3131)
- Guo Zheng (ORCID: https://orcid.org/0000-0001-6338-0192)
- Zhaoyou Wang (ORCID: https://orcid.org/0000-0001-8573-6970)
- Liang Jiang (ORCID: https://orcid.org/0000-0002-0000-9342)
- Yat Wong (ORCID: https://orcid.org/0000-0001-5912-7354)
Institutions
- University of Chicago (US)
Publication Details
- Journal
- Physical Review Letters
- Published
- 2025-05-19
- DOI
- https://doi.org/10.1103/physrevlett.134.200602
- Citations
- 2
- Primary Topic
- Matrix Theory and Algorithms
- Type
- article
- Field-Weighted Citation Impact
- 3.01
Funders
- National Science Foundation
- David and Lucile Packard Foundation
- U.S. Department of Energy
- Defense Advanced Research Projects Agency
- Multidisciplinary University Research Initiative
- Advanced Scientific Computing Research
- Air Force Office of Scientific Research
- Army Research Office