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Noise vs Noise: Continuous Quantum Tracking Without Wavefunction Collapse via Noise Field Measurement

AWATIF ALLHYANI

Published Apr 2, 2026• 0 citations
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Abstract

This work presents a novel quantum measurement scheme called "Noise vs Noise," where a quantum particle (electron) is never directly measured. Instead, we measure a reference noise field that is entangled with the electron. Using the POVM formalism, we demonstrate that the electron's position can be inferred from the noise statistics while the wavefunction remains partially coherent.

DOI
10.5281/zenodo.19377826

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This work presents a novel quantum measurement scheme called "Noise vs Noise," where a quantum particle (electron) is never directly measured. Instead, we measure a reference noise field that is entangled with the electron. Using the POVM formalism, we demonstrate that the electron's position can be inferred from the noise statistics while the wavefunction remains partially coherent.
One of the most fundamental principles of quantum mechanics is the collapse of the wave function upon measurement. Here, we present a novel approach called Noise vs Noise that enables continuous tracking of a quantum particle (specifically, an electron in a double-slit experiment) without causing wave function collapse. Instead of directly interacting with the particle, we introduce a well-defined reference noise field into the medium. The electron perturbs this noise through its electric field, and by analyzing the noise distortion, we extract information about the electron’s position and velocity. Numerical simulations demonstrate that the wave function remains intact (correlation = 1.0000) while achieving positional accuracy on the order of 10−8 m and velocity estimates within the correct order of magnitude (106 m/s). The uncertainty product ∆x · ∆p remains above the Heisenberg limit (ħ/2), confirming that the method re- spects quantum mechanical principles while offering a gentle measurement paradigm. This work opens new possibilities for quantum sensing, continuous monitoring, and fundamental tests of quantum mechanics.
We apply the formalism of quantum measurement theory to the idealized measurement of the position of a particle with an optical interferometer, finding that the backaction of counting entangled photons systematically collapses the particle’s wavefunction toward a narrow Gaussian wavepacket at the location xest determined by the measurement without appeal to environmental decoherence or other spontaneous collapse mechanism. Further, the variance in the particle’s position, as calculated from the post-measurement wavefunction, agrees precisely with shot-noise limited uncertainty of the measured xest. Both the identification of the absolute square of the particle’s initial wavefunction as the probability density for xest and the de Broglie hypothesis emerge as consequences of interpreting the intensity of the optical field as proportional to the probability of detecting a photon. Linear momentum information that is encoded in the particle’s initial wavefunction survives the measurement, and the pre-measurement expectation values are preserved in the ensemble average.
Even though measurement results obtained in the real world are generally both noisy and continuous, quantum measurement theory tends to emphasize the ideal limit of perfect precision and quantized measurement results. In this article, a more general concept of noisy measurements is applied to investigate the role of quantum noise in the measurement process. In particular, it is shown that the effects of quantum noise can be separated from the effects of information obtained in the measurement. However, quantum noise is required to ``cover up'' negative probabilities arising as the quantum limit is approached. These negative probabilities represent fundamental quantum-mechanical correlations between the measured variable and the variables affected by quantum noise.
According to the no-signaling theorem, the nonlocal collapse of the wavefunction of an entangled particle by the measurement on its twin particle at a remote location cannot be used to send useful information. Given that experiments on nonlocal correlations continue to have loopholes, we propose a stronger principle that the nonlocality of quantum mechanics itself is veiled. In practical terms, decoherence and noise compels us to view the wavefunction as representing knowledge of potential outcomes rather than the reality. Experimental evidence in favor of naked nonlocality would support the view of the wavefunction as an objective description of physical reality.
We consider a continuous measurement of a two-level system (double-dot) by weakly coupled detector (tunnel point contact nearby). While usual treatment leads to the gradual system decoherence due to the measurement, we show that the knowledge of the measurement result can restore the pure wavefunction at any time (this can be experimentally verified). The formalism allows to write a simple Langevin equation for the random evolution of the system density matrix which is reflected and caused by the stochastic detector output. Gradual wavefunction ``collapse'' and quantum Zeno effect are naturally described by the equation.
In classical mechanics, a natural way to simplify a many body problem is to ``replace'' some of the elements of the composite system with surrogate force fields. In the realm of quantum mechanics, however, such a description is rarely compatible with the formalism of the theory. Nevertheless, the quantum version of external field models---the so-called noise representations---can be employed in certain circumstances. The mathematics behind these models indicate that the appearing fields typically exhibit random fluctuations, hence, the name noise field is more apt. In principle, measuring a classical force field is a trivial task; all that is needed is a probe equipped with an accelerometer that can be moved around while taking the measure of forces that affect it. Unfortunately, an analogous method cannot work in the quantum case. As indicated by the theory, the result of any measurement performed on the quantum system affected by a noise field always appear as an average over fluctuations, therefore, it is impossible to observe the noise fluctuations by measuring the state of the probe. Here, we will demonstrate that this limitation can be circumvented and that it is possible to expose the noise field fluctuations to direct observation. This allows one to sample the noise trajectories (stochastic realizations), store them, and later use them to simulate the dynamics of open quantum systems affected by the noise.