Auditing setting-dependent temporal selection in Photonic Bell Tests & DI-QKD

[Christopher ONeil]

Dear members of the group,

Thank you, Alex, for adding me to this forum. I would like to share a recent paper analyzing a subtle temporal selection systematic in fast photonic Bell tests and high-rate Device-Independent Quantum Key Distribution (DI-QKD) pipelines.

To prevent any immediate misunderstanding: this work is not a speculative attempt to classically simulate spin, bypass Bell's theorem, or argue that the Bloch sphere is "mis-specified." It is a standard quantum metrology and hardware security audit paper characterizing a physical systematic—setting-dependent single-photon timing sags in active Electro-Optic Modulator (EOM) drivers—and its impact on tight-window, postselected coincidence channels.

In high-speed, active basis-switching setups, EOM transients draw capacitive currents of up to 2.0 A, inducing sub-nanosecond electronic ground bounce and dynamic PMD axes-splitting. These transients shift single-photon arrival tags by a few picoseconds. Under tight noise-filtering coincidence windows (such as 2w ≈ 300 ps in CW or high-rate channels), this tag shift pushes borderline photons outside the software window, acting as a physical, setting-dependent data selector that can systematically bias observed CHSH correlators.

My manuscript builds directly upon the setting-dependent selection framework of Parker (Emmerson, 2026) to model this timing systematic and establish a "zero-trust" monitoring protocol:

1. **Formal Selection Mapping:** I apply Parker's framework to timing tags, deriving sharp analytical total-variation bounds on the observed correlator inflation:

   S_obs <= 2 + 2*Delta_Q <= 2 + 6*D_Q <= 2 + 8*T_max

2. **Common-Mode Timing Lemma:** I prove that if the setting-dependent timing shift is common-mode (depends purely on the setting selection and is completely independent of the prior hidden polarization coordinate lambda), the accepted measures remain identical to the prior. Under this condition, the classical CHSH inequality cannot be violated (S_obs <= 2), mathematically separating benign common-mode delays from selection-relevant differential sags.

3. **DI-QKD Key Rate Vulnerability:** By implementing an outcome-dependent timing gate model on a quantum singlet state, I demonstrate that under narrow gates (w = 150 ps), unmodeled EOM sags systematically inflate the observed CHSH value, leading to a ~0.55% artificial inflation of the certified secure key rate (r_obs overestimating the true key rate r_true).

4. **Empirical Real-Time Audit:** To avoid introducing a new selection loophole via event-level data rejection, I propose a continuous in-situ monitoring protocol using an empirical Linear Program to solve for the binned dispersion (Delta_Q,X) directly from timing histograms. This monitor operates as a pre-specified block-level abort rule. I derive the statistical count threshold required to resolve setting-dependent timing centroids to a sub-picosecond level:

   N_det > 18 * (sigma_j / delta_t)^2

 Crucially, this event threshold scales quadratically with the detector timing jitter sigma_j. In modern state-of-the-art setups operating with optimized low-jitter SNSPDs (sigma_j ≈ 10 ps), the required event count to resolve a 1 ps centroid shift shrinks to just ≈ 1,800 events, making the continuous audit exceptionally fast and practical.

Answering the community's demand for open, reproducible code audits, I have published the fully calibrated, mid-point quadrature-integrated simulation engine and LP solver in a public repository. The core code includes an automated unit test verifying the Common-Mode Timing Lemma (confirming that setting-only sags yield exactly zero CHSH bias):
https://github.com/chris-oneil/photonic-bell-test-temporal-delay

I have attached the compiled PDF of the manuscript to this post. I would be highly appreciative of your scholarly feedback, critiques, and insights on both the theoretical framework and the calibrated simulation engine.

Warm regards,

Christopher O'Neil  
Independent Researcher  
Big Rapids, MI, USA

[Christopher ONeil]

I have posted a technical addendum addressing two physical objections that likely arise when evaluating the temporal selection framework.

1. The single-mode fiber mode-filtering objection. A natural response is that post-EOM single-mode collection fibers erase any spatial walk-off before photons reach the cryostat detectors. We derive the complete 2D Gaussian overlap integral at the fiber facet and show that this is incorrect: the walk-off is not erased but is converted directly into a setting-dependent coupling attenuation at the fiber input, a mechanism we term the Link-Loss Translation. The TV bounds remain invariant.

2. The thermal circularity trap. Continuous active EOM switching at 100 MHz generates ~5 W of dielectric heating in the RTP crystal, producing a steady-state center temperature rise of 20.94 K under 1D conduction (40.94 °C). This causes a catastrophic 12.7 rad phase drift, making continuous calibration protocols circular. We numerically solve the time-dependent heat equation and show that a Burst-Mode Gated Calibration Protocol (100-pulse bursts with 10 ms cooling) bounds thermal fluctuations to ΔT ≈ 10⁻⁴ K, nearly two orders of magnitude below the metrological safety threshold.

The compiled addendum PDF, Python scripts, derivations, and figures are available here:
https://github.com/chris-oneil/photonic-bell-test-temporal-delay/tree/main/addendum

Feedback welcome.

Christopher O'Neil
Independent Researcher
Big Rapids, MI, USA