# Frequentist-approach inspired theory of quantum random phenomena predicts signaling

## TL;DR

This paper explores how adopting a frequentist-inspired framework for quantum randomness, unlike the traditional Kolmogorov approach, could break the indistinguishability of quantum ensembles and enable superluminal signaling, challenging foundational principles.

## Contribution

It introduces a frequentist-inspired theory of quantum phenomena that suggests potential violations of the no-signaling principle, highlighting implications for quantum state representation.

## Key findings

- Changing to a frequentist framework lifts ensemble indistinguishability.
- Potential for superluminal communication arises under the new framework.
- Implications for the foundational understanding of quantum states.

## Abstract

Different ensembles of the same density matrix are indistinguishable within the modern Kolmogorov probability measure theory of quantum random phenomena. We find that changing the framework from the Kolmogorov one to a frequentist-inspired theory of quantum random phenomena -- a la von Mises -- would lift the indistinguishability, and potentially cost us the no-signaling principle (i.e., lead to superluminal communication). We believe that this adds to the recent works on the search for a suitable representation of the state of a quantum system. While erstwhile arguments for potential modifications in the representation of the quantum state were restricted to possible variations in the formalism of the quantum theory, we indicate a possible fallout of altering the underlying theory of random processes.