A Reconstruction of Michelson Interference from On--Off Detection Statistics

Abstract:This paper reconstructs the Michelson interference phenomenon based solely on the binary (on-off) statistics of a single-photon counter and macroscopic path-difference data, without the a priori assumptions of complex wave superposition or prior spectral information. In contrast to the conventional approach that assumes light as a continuous complex wave function and considers interference between them, this study focuses on the algebraic properties inherent in discrete detection statistics. We verify that the discrete response data collected across various path differences form a positive semi-definite matrix, and apply Herglotz's theorem to this result. Consequently, we show that the harmonic form of the interference fringe is not a consequence of adopting a wave model as an axiom, but rather it is uniquely decomposed into a cosine average of wavenumbers dictated by testable algebraic constraints satisfied by the statistical data. Through this approach, the logical basis of the interference phenomenon can be described by the characteristics of the binary data itself, perfectly aligning with the modern optical experimental environment that relies entirely on discrete event statistics.

arXiv:2610.19569 [quant-ph]

(or arXiv:2610.19569v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.19569 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.