CSS Threshold-Model BDD Monte Carlo with Distributed Coexistence Noise for Hollow-Core Fibers

Keywords: CSS, Hollow-Core-Fibers, Monte-Carlo

Abstract:

\begin{sloppypar}
Hollow-core fibers (HCFs) offer ultra-low nonlinearity and latency for quantum--classical coexistence, but residual spontaneous Raman scattering (SpRS) and four-wave mixing (FWM) induce phase-dominated noise over long spans. We present a single-file, reproducible methodology note: a physics-driven asymmetric, temporally correlated error model provided as in-document executable code, and bounded-distance-decoding (BDD) Monte Carlo with 95\% Wilson intervals for a length-\nexact{\simn} CSS threshold setting with correctable radius $t=10$ (representative of designs with minimum distance $d=21$). We replace an end-power heuristic with distributed integrals along the span, yielding monotone-in-length noise consistent with fiber physics. Under a \SI{\simL}{\kilo\meter} HCF with a \SI{\simpcl}{\dBm} co-propagating classical channel and \SI{\simsep}{\nano\meter} spectral separation, the in-document script yields baseline Pauli probabilities $p_Z^{\text{base}}\approx \allowbreak \val{\simpz}$ and $p_X^{\text{base}}\approx \allowbreak \val{\simpx}$. With Markov correlation $\rho=\nexact{\simrhoB}$, the BDD logical error is
\begin{align*}
P_L &= \val{\simpLB} \\
&\quad \text{with 95\% CI }[\val{\simpLBlo},\,\val{\simpLBhi}] \\
&\quad \text{over } \nexact{\simtrials}\ \text{trials (seed \nexact{\simseed})}.
\end{align*}
We extend the script with explicit sweep modes, an optional shared-state burst model, a tunable burst factor, runtime statistics, and strengthened statistical and modeling justification with appropriate citations. To preserve strict single-file self-containment we disable compile-time macro regeneration; verified re-run steps are provided later. For plot-data traceability of all presented sweeps, the artifact can emit PGFPlots coordinate blocks for \emph{all} figures/tables on request (rho, run-length, length, power, separation, eta). We render all plots directly in LaTeX from artifact-derived macros; for the rho-sweep we also list the exact coordinates used for Fig.~\ref{fig:plrho} in Table~\ref{tab:sensitivity}, matching the artifact's \texttt{--emit-pgf-rho} output.
\end{sloppypar}

Submission Number: 196