Born-Rule Deviations Tested on Quantum Processors

The Born rule, typically introduced as a quantum axiom, is shown to emerge as an equilibrium condition associated with modular (KMS) balance. We identify laboratory regimes where this balance can be weakly and controllably violated, and derive a universal, normalization-preserving correction to quantum measurement probabilities in the form of a modular exponential reweighting of Born amplitudes. The correction depends solely on experimentally reconstructed reduced states and outcome-resolved modular imbalance, and vanishes exactly under equilibrium, recovering the Born rule. We build a microscopic realization using standard von Neumann premeasurement, GKLS evolution of the apparatus, and projective readout, showing that the effect arises entirely within orthodox quantum mechanics without modifying unitary dynamics. The deviation leaves single-shot outcomes unchanged but induces a directed statistical bias visible only in large-N data. Locality and no-signalling hold, since in multipartite settings the correction depends only on the modular generator of the measured subsystem. We report experiments on IBM superconducting processors. First, full two-qubit Bell tomography confirms high-fidelity stabilizer correlations (E_ZZ, E_XX ≈ 0.98), validating reconstruction and establishing a Born-accurate baseline. Second, large-statistics three-qubit GHZ runs across multiple backends (ibm_fez, ibm_marrakesh, ibm_torino) show stable {000,111} sector frequencies under shot scaling, enabling extraction of preliminary modular tilt bounds. Finally, a controlled scaling study confirms 1/√N Born shot noise up to N = 20,000, while device biases remain roughly constant, establishing the metrological separation needed to detect nonequilibrium signatures. These results define a precision framework to estimate or constrain modular tilts on present-day platforms using raw (unmitigated) populations, tomography, and validated error models. They provide the first operational bounds on deviation parameters extracted from raw NISQ data in GHZ and Bell configurations, and outline a falsifiable protocol for future non-KMS driving experiments. The analysis explicitly separates statistical fluctuations from systematic bias through shot-scaling tests, enabling robust discrimination between equilibrium Born behavior and controlled nonequilibrium effects. This positions modular balance as an experimentally testable organizing principle linking quantum measurement statistics with nonequilibrium thermodynamics. Together, theory and data show that modular nonequilibrium deviations are experimentally accessible, tightly constrained, and operationally meaningful, suggesting that the Born rule may be the equilibrium shadow of a deeper thermodynamic structure in quantum theory.