Horizon-Induced Entanglement Sterilization as a Quantum-Limited Gaussian Amplifier Channel

This work analyzes the degradation of continuous-variable entanglement between an inertial reference mode (Alice) and a mode accessible to a noninertial observer (Rob) when horizon-induced mode splitting renders part of Rob's degrees of freedom inaccessible. Within an effective single-mode Gaussian description, tracing the inaccessible sector induces on Rob a local phase-insensitive Gaussian amplifier with gain g = cosh²r (quantum-limited when the environment is in vacuum), where r is the Unruh squeezing parameter. For a standard-form two-mode input we provide closed-form output covariance matrices and the logarithmic negativity EN, and we derive an exact threshold separating (i) a persistent large-r exponential tail EN ~ C·exp (−2r) from (ii) finite-r sudden death when additional thermal noise is present. In the quantum-limited pure-input case the prefactor is C (s) = 8·tanh² (s) /ln 2. We further show that, within this Gaussian truncation, the asymptotic scale of the entanglement tail is controlled by the effective modular temperature βR of Rob's reduced single-mode state. All quantitative claims are verified numerically. Connections to type-III algebraic modular theory and to semiclassical gravitational entropy are discussed as a delineated program rather than derived results; in particular, no identification of C (s) with A/4G or with the Bekenstein–Hawking entropy is claimed. A falsifiable analogue-gravity prediction (BEC or optical horizons) is given in terms of the time decay of the Hawking–partner logarithmic negativity. This preprint develops quantitatively a mechanism from the author's earlier work, "Incomplete Causal Transactions: Black Holes as Permanently Frustrated Couplers" (DOI: 10. 5281/zenodo. 18736657). AI use disclosure: AI systems were used as tools for symbolic and numerical verification of the Gaussian calculations and for reference checking; all quantitative claims were independently verified by direct computation, and the author takes full responsibility for the work and its delimited scope.