It is customary to see random interactions of particles and systems with each other as being the origin of noise. It is often used to describe the limits of experimental sensitivity in a physics experiment. A measurement is said to be in the noise if it is not reproducible.
A recently proposed local measurement axiom (Postulate M) replaces the instantaneous global projection of textbook quantum mechanics with branch selection triggered by completed local decoherence, while a companion ψ-ontic analysis identifies continuous spontaneous localization (CSL) as a concrete local mechanism for the selection itself. Here we test this two-stage account quantitatively in the Einstein–Podolsky–Rosen (EPR) scenario. We integrate the nonlinear CSL stochastic Schrödinger equation for an entangled spin pair in which one particle couples to a local spin bath with random couplings, bath self-dynamics, and intra-bath interactions, while the noise field and collapse operator act only at the measurement site. Analytically, we derive an exact law for the maximal Clauser–Horne–Shimony–Holt (CHSH) value under local decoherence, Smax(t)=21+sin2(2θ)∣z(t)∣2, with z(t) the decoherence factor and θ the entanglement angle: the CHSH excess over the classical bound is consumed, never the measurement-basis probabilities, which are exactly conserved. We further show that the selection stage is governed by an exact martingale: the branch weight obeys a scalar Itô equation whose derivation requires only the orthogonality of the branches—supplied by the spin structure, not by the environment—so the Born rule emerges as an absorption probability irrespective of the residual bath coherence. Numerically, the law holds to machine precision (∼ 10−15) for all three bath classes, including interacting environments, and through finite-size recurrences; stochastic trajectories confirm Born statistics to within sampling error, with all realizations fully resolved. The ensemble-averaged reduced state of the distant particle is invariant under the local collapse-operator axis and rate—parameter independence as a structural theorem, verified to machine precision in the unitary sector—and branch amplitudes are invariant across all environmental initial conditions and dynamics (∼ 10−11), confirming that outcome randomness is not of environmental origin. In the symmetric configuration, with independent noises at both wings, the two local noises provably drive a single global branch martingale at the summed rate: selection is one joint event whose absorbing states are the correlated branches—mismatched outcomes are dynamically excluded (zero events in 300 realizations, against ∼ 25% each for a product-state control)—the joint statistics are invariant under swapping which wing completes first (93% vs 9% orderings, distributions equal within sampling error), and sampled outcomes reproduce the singlet’s measurement correlation E(β) = − cos β—with β the angle between Alice’s and Bob’s measurement axes—including a CHSH value |S| = 2.710±0.073, consistent with the Tsirelson bound 2√2 within sampling errors. Decoherence and local stochastic selection jointly reproduce the empirical content of quantum measurement in the EPR scenario with no nonlocal dynamical element: the only nonclassical resource is the nonseparability of the initial state. Nonlocal projection is thus dispensable not only axiomatically and ontologically but operationally.
Abstract Collapse models including some external noise of unknown origin are routinely used to describe phenomena on the quantum-classical border; in particular, quantum measurement. Although containing nonlinear dynamics and thereby exposed to the possibility of superluminal signaling in individual events, such models are widely accepted on the basis of fully reproducing the non-signaling statistical predictions of quantum mechanics. Here we present a deterministic nonlinear model without any external noise, in which randomness—instead of being universally present—emerges in the measurement process, from deterministic irregular dynamics of the detectors. The treatment is based on a minimally nonlinear von Neumann equation for a Stern–Gerlach or Bell-type measuring setup, containing coordinate and momentum operators in a self-adjoint skew-symmetric, split scalar product structure over the configuration space. The microscopic states of the detectors act as a nonlocal set of hidden parameters, controlling individual outcomes. The model is shown to display pumping of weights between setup-defined basis states, with a single winner randomly selected and the rest collapsing to zero. Environmental decoherence has no role in the scenario. Through stochastic modelling, based on Pearle’s ‘gambler’s ruin’ scheme, outcome probabilities are shown to obey Born’s rule under a no-drift or ‘fair-game’ condition. This fully reproduces quantum statistical predictions, implying that the proposed non-linear deterministic model satisfies the non-signaling requirement. Our treatment is still vulnerable to hidden signaling in individual events, which remains to be handled by future research.
Running quantum programs is fraught with challenges on on today's noisy intermediate scale quantum (NISQ) devices. Many of these challenges originate from the error characteristics that stem from rapid decoherence and noise during measurement, qubit connections, crosstalk, the qubits themselves, and transformations of qubit state via gates. Not only are qubits not “created equal”, but their noise level also changes over time. IBM is said to calibrate their quantum systems once per day and reports noise levels (errors) at the time of such calibration. This information is subsequently used to map circuits to higher quality qubits and connections up to the next calibration point. This work provides evidence that there is room for improvement over this daily calibration cycle. It contributes a technique to measure noise levels (errors) related to qubits immediately before executing one or more sensitive circuits and shows that just-in-time noise measurements can benefit late physical qubit mappings. With this just-in-time recalibrated transpilation, the fidelity of results is improved over IBM's default mappings, which only uses their daily calibrations. The framework assess two major sources of noise, namely readout errors (measurement errors) and two-qubit gate/connection errors. Experiments indicate that the accuracy of circuit results improves by 3-304% on average and up to 400% with on-the-fly circuit mappings based on error measurements just prior to application execution.