bb84-noise-simulation

Abstract

We present a scalable stochastic simulator for the BB84 quantum key distribution (QKD) protocol that bridges the gap between the mathematical rigor of the density-matrix formalism and the computational tractability required for large-scale Monte Carlo analysis. Our core contribution is a systematic, analytically grounded translation of completely positive trace-preserving (CPTP) noise maps—including phase-damping, depolarization, and optical fiber attenuation—into probabilistic Pauli-error injection schemes compatible with the stabilizer circuit simulation paradigm implemented by the Stim library. We integrate Dynamical Decoupling (DD) sequences (Hahn Echo, CPMG-n) directly into the quantum memory model under the quasi-static noise assumption, capturing their decoherence suppression as a reduction in the effective Pauli-Z injection probability. Through Monte Carlo experiments comprising 105 shots per configuration averaged over K = 50 independent repetitions, we characterize the Quantum Bit Error Rate (QBER) and Secret Key Rate (SKR) as functions of fiber length L ∈ [1, 77] km under four DD conditions. Our results demonstrate that CPMG4 sequences suppress QBER by up to 70% at short distances and maintain statistically significant advantages over the unmitigated baseline across all tested ranges, with the SKR improvement reaching 36% at L = 25 km. This work provides a validated, computationally efficient simulation framework directly applicable to the design of fault-tolerant quantum network nodes. Keywords: BB84, quantum key distribution, density matrices, CPTP maps, Kraus operators, stabilizer simulation, Stim, dynamical decoupling, CPMG, Hahn echo, QBER, Monte Carlo.

1. Contributions

This work makes the following specific contributions:

1. Density-matrix-to-Pauli translation: We derive the exact correspondence between phase-flip, depolarizing, and bit-flip Kraus channels and their equivalent Pauli injection probabilities, enabling density-matrix-accurate noise modeling inside a stabilizer simulation (Section 2).
2. Stim as simulation backend: We justify the selection of the Stim library [10] over densitymatrix simulators (e.g., QuTiP, Qiskit Aer) via the Gottesman-Knill theorem and quantify the resulting speedup (Section 3).
3. Physical fiber and memory models: BeerLambert attenuation, distance-dependent depolarization, and T2 dephasing with exponential coherence decay (Section 4).
4. DD mitigation under quasi-static noise: Hahn Echo and CPMG-n sequences modeled analytically as reductions in effective dephasing probability (Section 5).
5. Statistically robust Monte Carlo: K = 50 independent repetitions per (L, DD) point, reporting mean ± standard error to suppress shot-noise artifacts at long distances (Section 6).