References

Em03A

N. Cheung, Em03-A: A Fixed-Background Hawking Emission Theorem, version 1, 8 October 2026. Supplied source 03-A-v1.tex. Used through its stated boundary prescription, :horizonoccupation, :quantumscatter, :numberdensity, and :packetlaw. Its manuscript proofs are not independently verified here.

LandmarkI

N. Cheung, I, version 1. Supplied characterization statement and excerpts: :strategy-class, :requirements, and :main. The characterization is an admitted semantic premise, not reproved in this paper.

DMP

C. Dappiaggi, V. Moretti, and N. Pinamonti, Rigorous construction and Hadamard property of the Unruh state in Schwarzschild spacetime, Advances in Theoretical and Mathematical Physics 15 (2011), 355–447. arXiv:0907.1034. The bulk-state construction is inherited through Em03-A.

Weedbrook

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Gaussian Quantum Information, Reviews of Modern Physics 84 (2012), 621–669. arXiv:1110.3234. doi:10.1103/RevModPhys.84.621. General Gaussian-state context; the finite-mode identifications used here are proved explicitly.

GardinerCollett

C. W. Gardiner and M. J. Collett, Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation, Physical Review A 31 (1985), 3761–3774. doi:10.1103/PhysRevA.31.3761.

YamamotoJames

N. Yamamoto and M. R. James, Zero-dynamics principle for perfect quantum memory in linear networks, New Journal of Physics 16 (2014), 073032. arXiv:1403.1698. doi:10.1088/1367-2630/16/7/073032. Pulse-selective linear-memory context, not a proof of the particular Hawking capture model.

Shirokov

M. E. Shirokov, Energy-constrained diamond norms and their use in quantum information theory, Problems of Information Transmission 54 (2018), 20–33. arXiv:1706.00361. doi:10.1134/S0032946018010027. The constraints used in this paper are explicitly oscillator occupation constraints.

Krastanov

S. Krastanov, V. V. Albert, C. Shen, C.-L. Zou, R. W. Heeres, B. Vlastakis, R. J. Schoelkopf, and L. Jiang, Universal Control of an Oscillator with Dispersive Coupling to a Qubit, Physical Review A 92 (2015), 040303(R). arXiv:1502.08015. doi:10.1103/PhysRevA.92.040303. A comparison for a different control set, not a compiler or leakage certificate for the number-selective primitives here.

FewsterVerch

C. J. Fewster and R. Verch, Quantum fields and local measurements, arXiv:1810.06512, published version. Used for the separate local system–probe measurement obligation, not to identify the present Markov port with a local scalar-field apparatus.

Watrous

J. Watrous, The Theory of Quantum Information, Cambridge University Press, 2018. Chapters 2 and 3: channels, instruments, trace distances, and the completely bounded trace norm. The specific channel identities and distance formulas in this manuscript are proved directly.