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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2605.29820 |
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| _version_ | 1866911728284991488 |
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| author | Wang, Kun |
| author_facet | Wang, Kun |
| contents | Certifying the fidelity of a prepared state to a target stabilizer state is a fundamental task in quantum information processing. Ref. [Phys. Rev. A 99, 042337 (2019)] gave the optimal worst-case lower bound from one fixed stabilizer generator gauge, but gauge dependence can leave a large fidelity ambiguity. We develop an adaptive extension that reports the full certified fidelity interval. First, for a single gauge, we derive the complementary optimal worst-case upper bound. We then formulate gauge selection as an adaptive design problem in which each round solves exact endpoint linear programs and chooses a new gauge by a witness elimination policy. We prove monotonic tightening, exact recovery once all nontrivial stabilizers are covered, and the worst-case necessity of full coverage. Finally, we identify structured syndrome distributions for which adaptivity beats this exponential benchmark, and we numerically confirm faster concentration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_29820 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Adaptive Stabilizer State Fidelity Certification Wang, Kun Quantum Physics Certifying the fidelity of a prepared state to a target stabilizer state is a fundamental task in quantum information processing. Ref. [Phys. Rev. A 99, 042337 (2019)] gave the optimal worst-case lower bound from one fixed stabilizer generator gauge, but gauge dependence can leave a large fidelity ambiguity. We develop an adaptive extension that reports the full certified fidelity interval. First, for a single gauge, we derive the complementary optimal worst-case upper bound. We then formulate gauge selection as an adaptive design problem in which each round solves exact endpoint linear programs and chooses a new gauge by a witness elimination policy. We prove monotonic tightening, exact recovery once all nontrivial stabilizers are covered, and the worst-case necessity of full coverage. Finally, we identify structured syndrome distributions for which adaptivity beats this exponential benchmark, and we numerically confirm faster concentration. |
| title | Adaptive Stabilizer State Fidelity Certification |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2605.29820 |