The Born rule is usually introduced as an axiomatic postulate of quantum mechanics, assigning outcome probabilities as squared wavefunction amplitudes without an underlying physical mechanism. While recent theoretical work has suggested that Born statistics may emerge dynamically from a pre-locking regime in quantum measurement, direct experimental validation on physical hardware has remained an open question. In this work, we present hardware-empirical evidence that Born statistics arise as a stable fixed point of recursive quantum realization. Using real superconducting quantum processors (IBM Quantum), we implement a discrete analogue of continuous measurement based on recursive weak probing with ancilla qubits, while keeping the prepared quantum state strictly fixed. By varying the number of weak probe interactions prior to final projective measurement, we observe a systematic evolution of outcome statistics. As probing depth increases, the measured probabilities converge toward the Born prediction for the prepared state. Crucially, this convergence is suppressed in control experiments that remove probe coupling or scramble relative phase, despite identical circuit depth and gate counts. These results rule out explanations based on instantaneous collapse, circuit depth, classical noise, or readout bias. Instead, they support a physical picture in which quantum probabilities emerge dynamically through coherent, recursive stabilization of competing realizations during measurement. This work provides a direct hardware counterpart to earlier theoretical models of emergent Born statistics and demonstrates that probabilistic quantum outcomes can be experimentally traced to a structured, pre-realizational process rather than postulated as fundamental.
The Born rule is usually introduced as an axiomatic postulate of quantum mechanics, assigning outcome probabilities as squared wavefunction amplitudes without an underlying physical mechanism. While recent theoretical work has suggested that Born statistics may emerge dynamically from a pre-locking regime in quantum measurement, direct experimental validation on physical hardware has remained an open question. In this work, we present hardware-empirical evidence that Born statistics arise as a stable fixed point of recursive quantum realization. Using real superconducting quantum processors (IBM Quantum), we implement a discrete analogue of continuous measurement based on recursive weak probing with ancilla qubits, while keeping the prepared quantum state strictly fixed. By varying the number of weak probe interactions prior to final projective measurement, we observe a systematic evolution of outcome statistics. As probing depth increases, the measured probabilities converge toward the Born prediction for the prepared state. Crucially, this convergence is suppressed in control experiments that remove probe coupling or scramble relative phase, despite identical circuit depth and gate counts. These results rule out explanations based on instantaneous collapse, circuit depth, classical noise, or readout bias. Instead, they support a physical picture in which quantum probabilities emerge dynamically through coherent, recursive stabilization of competing realizations during measurement. This work provides a direct hardware counterpart to earlier theoretical models of emergent Born statistics and demonstrates that probabilistic quantum outcomes can be experimentally traced to a structured, pre-realizational process rather than postulated as fundamental.
This work presents empirical evidence that quantum measurement is not an instantaneous, structureless collapse, but a multi-stage recursive realization process governed by coherence, weak predictability, and global structural constraints. Using real superconducting quantum processors (IBM Quantum), a sequence of controlled experiments probes four distinct stages of realization:(I) pre-realizational structural orientation,(II) weak predictive bias accessed through ancilla measurements,(III) recursive stabilization via repeated weak probing, and(IV) topology-dependent anti-locking that suppresses locally stable but globally inconsistent configurations. The experiments demonstrate that weakly coupled ancilla qubits acquire statistically significant information about final outcomes prior to projective measurement, that this information disappears under controlled decoupling and phase scrambling, and that repeated probing progressively stabilizes outcome tendencies. Crucially, closed-ring circuit topologies exhibit significantly stronger suppression of locally “locking” configurations than open-line controls, despite identical gate parameters, depth, and hardware backend. This topology-dependent anti-locking effect cannot be explained by local noise, readout bias, or marginal statistics, and instead indicates the presence of a global coherence constraint acting during realization. The results support a physical interpretation in which quantum states represent pre-realizational structure, analogous to an architectural plan, while measurement corresponds to the completion of a recursive, globally constrained selection process rather than an abrupt collapse. Beyond foundational implications, the work demonstrates that contemporary quantum hardware can function as an experimental platform for probing the internal structure of quantum theory itself, opening new avenues for empirical studies of realization, consistency, and emergence.
This work presents an operational and falsifiable mechanism by which Born statistics emerge dynamically from continuous quantum measurement, without assuming wavefunction collapse or probabilistic postulates. Instead of treating the Born rule as a fundamental axiom, outcome probabilities are shown to arise from the pre-locking dynamical structure of measurement trajectories. Using stochastic quantum trajectory simulations of continuously monitored qubit systems, the study introduces the concept of a locking time, defined as the moment at which measurement dynamics irreversibly stabilizes into a definite outcome. Crucially, this locking transition is preceded by a finite pre-locking regime in which multiple outcome configurations coexist and compete dynamically. To quantify this competition, a structural robustness functional is defined as the time-integrated stability of each outcome configuration prior to locking. Normalized robustness values provide a dynamical prediction for final measurement outcomes using only pre-locking information. These predictions exhibit statistically significant correlation with observed outcomes before locking occurs, while the same construction applied after locking shows no predictive power, providing a falsifiable internal control. The mechanism is demonstrated to be robust across wide ranges of measurement strength and decoherence parameters and is shown to be independent of the measurement basis, reproducing the same behavior for measurements performed in both σz and σx bases. No fine tuning or hidden-variable assumptions are required. These results support a reinterpretation of the Born rule as an emergent statistical consequence of measurement dynamics, rather than a fundamental principle. Probabilities arise from accumulated dynamical stability during the measurement process itself, shifting the role of probability in quantum mechanics from an axiom to an operational outcome of pre-locking structural competition.
This work investigates the physical origin of the Born rule in quantum mechanics from an operational perspective. Instead of postulating probabilistic measurement outcomes as fundamental, the paper demonstrates that Born-rule statistics can emerge naturally from continuous measurement dynamics combined with noisy amplification and threshold detection. Focusing on superconducting qubit dispersive readout, the measurement process is modeled as a drift–diffusion (Langevin) dynamics of an integrated readout signal, followed by symmetric thresholding. The resulting outcome probabilities are shown to follow an exact sigmoidal (logistic) form derived from a first-passage-time problem. By analyzing the linear-response regime around maximal uncertainty, it is demonstrated analytically that the standard Born rule is reproduced when the effective signal-to-noise parameter of the readout chain satisfies a specific optimal condition. Outside this regime, the model predicts systematic, non-linear deviations in the probability distribution, particularly in the saturation (tail) regions. The framework is fully compatible with modern circuit QED experiments and makes concrete, falsifiable predictions for superconducting qubit platforms. The results suggest that quantum probabilities may be understood as an emergent operational fixed point of realistic measurement hardware, rather than as a purely axiomatic feature of the wavefunction.
Abstract 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.
The predictions of quantum mechanics are probabilistic. Quantum probabilities are extracted using a postulate of the theory called the Born rule, the status of which is central to the problem of quantum mechanics. Efforts to justify the Born rule from other physical principles, and thus elucidate the measurement process, have involved lengthy statistical or information-theoretic arguments. Here we show that Bohm's deterministic formulation of quantum mechanics allows the Born rule for measurements on a single system to be derived, without any statistical assumptions. We solve a simple example where the creation of an ensemble of identical quantum states, together with position measurements on those states, are described by Bohm's quantum dynamics. The calculated measurement outcomes agree with the Born-rule probabilities, which are thus a consequence of deterministic evolution. Our results demonstrate that quantum probabilities can emerge from simple dynamical laws alone, and they support the view that there is no underlying indeterminism in quantum phenomena.
The predictions of quantum mechanics are probabilistic. Quantum probabilities are extracted using a postulate of the theory called the Born rule, the status of which is central to the "measurement problem" of quantum mechanics. Efforts to justify the Born rule from other physical principles, and thus elucidate the measurement process, have involved lengthy statistical or information-theoretic arguments. Here we show that Bohm's deterministic formulation of quantum mechanics allows the Born rule for measurements on a single system to be derived, without any statistical assumptions. We solve a simple example where the creation of an ensemble of identical quantum states, together with position measurements on those states, are described by Bohm's quantum dynamics. The calculated measurement outcomes agree with the Born-rule probabilities, which are thus a consequence of deterministic evolution. Our results demonstrate that quantum probabilities can emerge from simple dynamical laws alone, and they support the view that there is no underlying indeterminism in quantum phenomena.