Passive spectral-admittance bounds and exact continuum certificates for multiresonator quantum-memory interfaces

Abstract: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 $\mathcal{B}$ is $1-\int_{\mathcal{B}} |r(i\omega)|^2 |f(\omega)|^2\,d\omega$, and the worst-case write efficiency is $1-\|r\|_{L^\infty(\mathcal{B})}^2$. We prove that a finite passive rational interface cannot have zero reflection on a nonzero interval and derive the Bode--Fano floor $\|r\|_\infty \geq \exp[-\pi\kappa/(2B)]$ 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 $\kappa=2$ and $B=1$, an 11-mode design obeys $0.064112405 \leq \|r\|_\infty < 0.0641125$, 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.

11 pages, 4 figures. Includes exact computer-assisted continuum certificates based on Sturm root counting and Routh--Hurwitz determinants

arXiv:2607.10704 [quant-ph]

(or arXiv:2607.10704v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.10704 Focus to learn more arXiv-issued DOI via DataCite

code/compute_tables.py

code/exact_certificate.py

code/independent_verifier.py

code/make_figures.py

code/make_interface_schematic.py

code/measure_seeded_certificates.py

code/reproduce.py

code/robustness_simulation.py

code/verify_sharpness.py

data/designs.json

environment-lock.md

requirements.txt

tests/test_core.py

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