Is the Born rule a result of measurement noise?

TL;DR

This paper explores whether the Born rule in quantum mechanics can be derived from measurement noise modeled as a stochastic process, suggesting noise may be fundamental to quantum measurement outcomes.

Contribution

It proposes a novel explanation for the Born rule based on stochastic dynamics during measurement, linking noise to quantum probability distributions.

Findings

Models measurement as a random walk in state space

Connects stochastic unitary matrices to measurement outcomes

Raises questions about experimental verification of the mechanism

Abstract

The Born rule asserts the probability distribution of eigenstates observed in unbiased quantum measurements, but the reason it holds remains elusive. This manuscript discusses how the Born rule might be explained by Schrodinger equation dynamics, if a measurement comprises a system responding to random fluctuations until it is within an arbitrarily small tolerance of a measurement eigenstate. We describe the random walk dynamics that produce this behavior in terms of a class of time-dependent, stochastic unitary matrices U(t). We also discuss the class of stochastic potential energies in the Schrodinger equation that is equivalent to this class of unitary matrices. This analysis raises some questions worth considering, including how to determine if any measurements actually follow the predicted random walk mechanism and whether a reliable measurement apparatus could be designed that deviates from Born rule probabilities. Interestingly, if any measurements do follow this random walk mechanism, then exposing a quantum system to stochastic 'noise' is an intrinsic part of such a measurement, not merely an unwanted side effect. This characteristic would have implications for reducing noise in quantum sensing and quantum computing. This is a draft of a work in progress. Questions and suggestions are welcome.