Optimal local recovery cannot alter critical orthogonality exponents in quantum spin environments

Abstract

We prove a local amplitude-ratio bound for positive ground states and an explicit reverse comparison for fidelity under finite-region erasure. An exact lattice calculation for a connected critical Ising chain gives amplitude exponent 1/8, preserved by arbitrary optimal control on any fixed spin set and, at the level of logarithmic exponents, on o(log N) spins. We derive the finite Cauchy product and its uniform strip asymptotics, and document exact two-spin optimization and an interferometric protocol for measuring the recovery. A separate finite-mediator theorem quantifies local compression and a decoder while retaining the rest of the environment exactly. We also give a ground-preparation Ramsey bound, counterexamples to stronger projected-state inferences, and independent full-Hamiltonian calculations.

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BibTeX RIS

BibTeX

@misc{zhao2026optimal,
  title = {{Optimal local recovery cannot alter critical orthogonality exponents in quantum spin environments}},
  author = {Zhixuan Zhao and Jun Li},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.39528},
  eprint = {2609.39528},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.39528},
}

RIS

TY  - UNPB
TI  - Optimal local recovery cannot alter critical orthogonality exponents in quantum spin environments
AU  - Zhixuan Zhao
AU  - Jun Li
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.39528
UR  - https://arxiv.org/abs/2609.39528
AB  - We prove a local amplitude-ratio bound for positive ground states and an explicit reverse comparison for fidelity under finite-region erasure. An exact lattice calculation for a connected critical Ising chain gives amplitude exponent 1/8, preserved by arbitrary optimal control on any fixed spin set and, at the level of logarithmic exponents, on o(log N) spins. We derive the finite Cauchy product and its uniform strip asymptotics, and document exact two-spin optimization and an interferometric protocol for measuring the recovery. A separate finite-mediator theorem quantifies local compression and a decoder while retaining the rest of the environment exactly. We also give a ground-preparation Ramsey bound, counterexamples to stronger projected-state inferences, and independent full-Hamiltonian calculations.
ER  -

Abstract

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