On spooky action at a distance and conditional probabilities

TL;DR

This paper explores the analogy between classical dependent probabilities and quantum entangled states, highlighting how measurements affect system states and probabilities in both contexts.

Contribution

It explicitly compares classical and quantum systems, clarifying how observations influence states and probabilities in each framework.

Findings

Classical and quantum measurement processes are analogous in how they update states.

Post-measurement states in quantum systems encode both state change and probability update.

Conditional probabilities are central to understanding measurement effects in both classical and quantum systems.

Abstract

The aim of this expos\'e is to make explicit the analogy between the classical notion of non-independent probability distribution and the quantum notion of entangled state. To bring that analogy forth, we consider a classical systems with two dependent random variables and a quantum system with two components. In the classical case, afet observing one of the random variables, the underlying sample space and the probability distribution change. In the quantum case, when and event pertaining to one of the components is observed, the post-measurement state captures, both, the change in the state of the system and implicitly the new probability distribution. The predictions after a measurement in the classical case and in the quantum case, have to be computed with the conditional distribution given the value of the observed variable.