2026/07/31 by Maxim V. Churilov
Physics and Astronomy · #quant-ph
11 pages, 4 figures. Includes exact computer-assisted continuum certificates based on Sturm root counting and Routh--Hurwitz determinants
arxiv created 2026/08/05 · arxiv updated 2026/08/06
Broadband quantum-memory interfaces are often assessed by center-frequency impedance matching or by a sampled efficiency curve. Neither supplies an operational continuous-band certificate, and absorption is not automatically reversible storage. We model a passive one-port multiresonator interface by a positive-real spectral admittance with explicitly identified controlled output channels. If their one-photon subspace is mapped isometrically into long-lived registers, the write probability for a normalized spectrum f supported in a band B is 1-∫B |r(iω)|2 |f(ω)|2 dω, and the worst-case write efficiency is 1-‖r‖L^∞(B)2. We prove that a finite passive rational interface cannot have zero reflection on a nonzero interval and derive the Bode--Fano floor ‖r‖_∞ ≥ exp[-πκ/(2B)] for a band of half-width B. At fixed pole locations, minimax synthesis is a quasiconvex semi-infinite problem in the oscillator strengths. We then give an exact computer-assisted certificate: after a decimal design is converted into an explicit rational system, the continuum reflection bound becomes positivity of one univariate polynomial and is proved by Sturm root counting; exact Routh--Hurwitz determinants certify stability and minimum phase. In units κ=2 and B=1, an 11-mode design obeys 0.064112405 ≤ ‖r‖_∞ < 0.0641125, implying a conditional uniform write guarantee above 0.995889587. This is a reproducible certificate for a specified interface, not a claim of global movable-pole optimality or of an experimentally complete memory.