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

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
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preprint

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

Gabriel Skura Ribeiro
Zenodo (CERN European Organization for Nuclear Research)
Quantum Information and Cryptography
preprint

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

Gabriel Skura Ribeiro
preprint en

Abstract

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.

Zenodo (CERN European Organization for Nuclear Research)
Quantum Information and Cryptography
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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 — Gabriel Skura Ribeiro · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS