A Sharp Fisher-Information Inequality for Boolean Pairs: Proof of the Amari--Kobayashi Conjecture

@misc{chen2026sharp,
  title = {{A Sharp Fisher-Information Inequality for Boolean Pairs: Proof of the Amari--Kobayashi Conjecture}},
  author = {Jun Chen and Shun Watanabe and Lei Yu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39355},
  eprint = {2610.39355},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.39355},
}

TY  - UNPB
TI  - A Sharp Fisher-Information Inequality for Boolean Pairs: Proof of the Amari--Kobayashi Conjecture
AU  - Jun Chen
AU  - Shun Watanabe
AU  - Lei Yu
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.39355
UR  - https://arxiv.org/abs/2610.39355
AB  - Consider two terminals that observe correlated uniform binary vectors and separately compress their observations to one bit. We prove that, for every blocklength and every correlation parameter in (−1,1), the Fisher information retained by the resulting pair of bits is maximized by matching parity functions of an appropriate degree, thereby resolving a conjecture of Amari and Kobayashi. The proof combines a Fourier-based bound on the derivative of the normalized covariance with a scalar inequality for signed polynomials subject to a global range constraint.
ER  -