IT FROM A: A Numerical and Analytic Companion to "No-Signalling Fixes the Hilbert-Space Inner Product" — Adversarial Mapping, a Universal Linear Coefficient, and a General Holographic Immunity Theorem
Pati (2026) proved analytically that any generalized Hilbert-space inner product with positive operator A≠I permits superluminal signaling, uniquely fixing the standard inner product as the only one consistent with relativistic causality. We provide a numerical and analytic companion to this result. Using adversarial variational search over an EPR-steering protocol, we confirm zero signal at A=I to machine precision, find nonzero signal at every tested deviation down to 10⁻⁶ with no safe region at any scale, determine the universal leading-order coefficient (exactly 1.000000, confirmed to 8 decimal places), show the same structure persists from qubits to qutrits, and find that the optimal metric deviation and optimal probe observable are exactly orthogonal on the Bloch sphere. Extending the protocol to a logical Bell pair between two [[5,1,3]] holographic code blocks, we prove and numerically confirm an exact immunity theorem: the signal vanishes identically when the inner-product deformation is confined to k physical qubits for k=1,2, and becomes genuinely nonzero exactly at k=3 — precisely the code's erasure-correction threshold. We show this generalizes, without further computation, to every quantum error-correcting code, via the general erasure-correction theorem of Knill-Laflamme and Bennett-DiVincenzo-Smolin-Wootters — resting on the same mathematical foundation used to derive the Ryu-Takayanagi holographic entanglement-entropy formula from quantum error correction. Simulation/computation-only results; no hardware component.
Authors
- Gabriel Skura Ribeiro (ORCID: https://orcid.org/0009-0003-5070-5260)
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-08-25
- DOI
- https://doi.org/10.5281/zenodo.22100194
- Primary Topic
- Quantum Information and Cryptography
- Type
- preprint