Entanglement Symmetry, Amplitudes, and Probabilities: Inverting Born's Rule

TL;DR

This paper explores how symmetries in entangled quantum states relate to probability amplitudes, deriving Born's rule by linking amplitudes to the square root of relative frequencies of sequences.

Contribution

It demonstrates that the amplitude of a superposition state is proportional to the square root of the relative frequency of sequences sharing the same total count, providing a novel derivation of Born's rule.

Findings

Amplitude proportional to square root of relative frequency

Symmetry (envariance) implies equiprobability of outcomes

Derivation of Born's rule from sequence amplitudes

Abstract

Symmetry of entangled states under a swap of outcomes ("envariance") implies their equiprobability, and leads to Born's rule. Here I show that the amplitude of a state given by a superposition of sequences of events that share same total count (e.g., n detections of 0 and m of 1 in a spin 1/2 measurement) is proportional to the square root of the fraction - square root of the relative frequency - of all the equiprobable sequences of 0's and 1's with that n and m.