Emergence of the Born rule in quantum optics

Abstract

The Born rule provides a fundamental connection between theory and observation in quantum mechanics, yet its origin remains a mystery. We consider this problem within the context of quantum optics using only classical physics and the assumption of a quantum electrodynamic vacuum that is real rather than virtual. The connection to observation is made via classical intensity threshold detectors that are used as a simple, deterministic model of photon detection. By following standard experimental conventions of data analysis on discrete detection events, we show that this model is capable of reproducing several observed phenomena thought to be uniquely quantum in nature, thus providing greater elucidation of the quantum-classical boundary.

Timelessness Strictly inside the Quantum Realm

“…Born’s rule has also been shown to result from picking outcomes with threshold detectors in a natural way from classical random signals for ergodic processes [ 125 , 126 ]. Some measure of stochastic ingredient is indispensable to arrive at Born’s rule; this might even be the unknown and fleeting exact timing since the beginning of the universe or some random background field [ 127 , 128 ].…”

Do photon-number-resolving detectors provide valid evidence for the discrete nature of light?

“…As previously mentioned, many physical effects considered to be explained exclusively by a dualistic photon picture have now acquired classical explanations. The use of approaches that consider common, unavoidable nuances of experimental and data analytic techniques such as arbitrary coincidence windows or post selection etc., may enable explanation of fundamental quantum phenomena such as the Born rule [72,84], quantum eraser, [85] entanglement itself, [86] or various Bell-type inequalities [87][88][89] with straightforward intuitable resolutions. [90][91][92][93][94][95][96][97][98][99][100][101][102] Needless to say, possible oversight regarding the foundational interpretations of instrument output can have farreaching effects not only on aspects of quantum computational advantage and quantum communication security, but also on basic physical effects regarded as exclusively quantum.…”

“…In addition to the experimental data produced, we also developed a script that generates detection events according to a classical model with a stochastic vacuum field component combined with deterministic amplitudethreshold detectors [72,73]. The classical nature of the model was an intentional feature used to test the possibility of reproducing what is typically interpreted as evidence for the particle nature of light via PNR detectors under purely continuous electromagnetic field conditions.…”

Entanglement and impropriety

“…For classical observables, a specific definition of measurement is needed to compute the correlations C i j , and for this we used local amplitude threshold crossings as a model for single-photon detection [15,16]. In this approach, a detection of the modal component b i is said to occur when |b i | > γ for some fixed amplitude threshold γ ≥ 0.…”

“…The present work generalizes prior research to arbitrary multi-modal squeezed states arising from symmetric squeezing matrices and examines the relationship to improper complex Gaussian random variables. In addition, the behavior under a deterministic model of photon detection is considered [13][14][15][16], which is an approach the previous work had not considered. Although Gaussian states may in some respects be deemed classical, the introduction of a nonlinear measurement scheme, such as we consider, when combined with post-selection can give rise to contextuality and, hence, quantum-like behavior such as violations of the Bell-CHSH inequality [15,17,18].…”