Bell Tests Achieve Relaxed Bounds with Preparation Nonstationarity on Superconducting Qubits

Bell tests on superconducting processors typically rely on the assumption that each circuit execution samples a consistent and unchanging preparation state, but new research challenges this fundamental principle. Prosanta Pal from Clemson University, Shubhanshu Karoliya from the Indian Institute of Technology Mandi, Gargee Sharma from the Indian Institute of Technology Delhi, and Ramakrishna Podila from Clemson University, alongside their colleagues, demonstrate that this assumption is frequently violated in current hardware. Their work reveals that slow drifts in the preparation process create context-dependent ensembles, potentially leading to misinterpreted results and a relaxation of established Bell inequality bounds. This discovery is significant because it identifies a previously unrecognised loophole in Bell tests on noisy intermediate-scale quantum devices, demanding the development of more robust and drift-aware experimental protocols to ensure reliable certification of quantum behaviour. The team’s operational witness, based on analysing outcome statistics, provides a means of detecting this preparation nonstationarity and distinguishing it from measurement errors.

Preparation Nonstationarity and Relaxed Bell Inequalities Researchers have

The study addressed a critical assumption within Bell and Clauser-Horne-Shimony-Holt (CHSH) tests performed on superconducting processors: that repeated circuit executions sample a single, stationary preparation ensemble. Researchers demonstrated that this assumption is frequently violated in contemporary hardware, directly impacting the interpretation of observed Bell violations. To account for this, the team introduced an ensemble-divergence framework, positing that slow temporal drift in the preparation process creates context-dependent effective ensembles, even while preserving measurement independence and locality.

This led to a relaxed Bell bound of |S| ≤ 2 + 6δens, where δens quantifies the degree of preparation nonstationarity. Recognising that δens is not directly measurable, scientists developed an operational witness based on bin-resolved outcome statistics for fixed measurement channels. Experiments employed Pauli-axis measurements on superconducting processors to observe statistically significant operational drift, persisting even after full two-qubit readout mitigation, effectively ruling out measurement artifacts as the source of the observed discrepancies.

Crucially, drift extracted from CHSH-optimal measurements was eliminated by mitigation techniques, demonstrating the unsuitability of these settings for diagnosing preparation nonstationarity. The research further established that observed Bell violations imply only modest ensemble divergences, comparable in scale to those required in Hall-type measurement-dependence models, but arising solely from preparation drift combined with experimental scheduling. The team meticulously matched Monte Carlo (MC) null models and noise-calibrated simulations to validate their findings.

This work identifies a preparation-dependent loophole relevant to Bell tests on noisy intermediate-scale devices and underscores the necessity of drift-aware protocols for reliable certification of quantum systems. The innovative methodology enables a more nuanced understanding of Bell violations, distinguishing between preparation-related effects and genuine quantum non-locality.

State Drift Violates Bell Test Assumptions

Scientists have demonstrated that the standard assumptions underpinning Bell tests on superconducting processors can be violated due to slow temporal drift in the preparation of quantum states. The research reveals that repeated circuit executions do not necessarily sample a single, stationary preparation ensemble, a critical consideration for interpreting observed Bell violations. The team introduced an ensemble-divergence framework, quantifying preparation nonstationarity with a parameter denoted as δens, which relaxes the standard Bell bound to |S| ≤ 2 + 6δens.

Experiments were conducted using Pauli-axis measurements on superconducting processors, specifically the ibm_fez and ibm_torino systems. Measurements confirmed statistically significant operational drift, quantified by δop, that persisted even after applying full two-qubit readout mitigation techniques, effectively ruling out measurement artifacts as the source of the observed discrepancies. In contrast, drift extracted from CHSH-optimal measurements was eliminated by mitigation, indicating these settings are unsuitable for diagnosing preparation nonstationarity.

This finding highlights the importance of carefully selecting measurement configurations for accurate assessment of preparation fidelity. Data shows that the observed Bell violations imply only modest ensemble divergences, comparable in scale to those required in Hall-type measurement-dependence models. However, the team established that this divergence arises solely from preparation drift combined with the experimental scheduling of the quantum circuits. This breakthrough delivers a preparation-dependent loophole relevant to Bell tests on noisy intermediate-scale quantum devices, challenging the conventional interpretation of Bell violations.

Tests prove that the observed drift is not merely a technical artifact but a fundamental consequence of the dynamic nature of the preparation process. The research identifies the necessity of drift-aware protocols for reliable quantum certification, paving the way for more robust and accurate tests of quantum mechanics on near-term quantum hardware. The work establishes a clear link between temporal fluctuations in control parameters and the observed non-stationary outcome statistics, offering a novel perspective on the challenges of performing Bell tests on superconducting platforms.

Preparation Nonstationarity and Bell Inequality Violation

This research investigated the role of preparation nonstationarity in Bell and CHSH experiments conducted on superconducting quantum processors. By relaxing the standard assumption of a single, unchanging preparation ensemble, while maintaining locality and measurement independence, the authors derived a modified Bell inequality that accounts for ensemble divergence. This framework identifies a preparation-dependent loophole, distinct from previously understood measurement dependence, and directly linked to known non-i.i.d. effects present in superconducting hardware.

Operationally, the researchers introduced a metric, δop, to witness preparation nonstationarity using readily obtainable outcome statistics. Experiments on superconducting processors revealed statistically significant drift, persisting even after mitigation of two-qubit readout errors, thereby confirming δens greater than zero. Importantly, the observed Bell violations imply a minimal ensemble divergence comparable in scale to those invoked in models of measurement dependence, but arising solely from preparation drift and experimental scheduling.

The authors acknowledge that δens cannot be directly inferred from operational data, and that the observed effects are influenced by the specific experimental setup. They suggest future work should focus on developing drift-aware experimental protocols and diagnostics for reliable quantum certification. Their findings demonstrate that Bell violations on current noisy intermediate-scale quantum hardware can occur alongside a breakdown in the assumption of preparation stationarity, highlighting a crucial consideration for interpreting results from these devices.