On the EPR paradox in systems with finite number of levels (Revised)

TL;DR

This paper reexamines the EPR paradox in finite-level systems, highlighting how measurements alter the state and probabilities, simplifying analysis while preserving core quantum features.

Contribution

It demonstrates that finite-level systems allow clearer analysis of the EPR paradox by focusing on measurement-induced state changes without the complexities of continuous systems.

Findings

Measurement changes the compatible microscopic states.

Quantum predictions depend on the measured observable.

Finite systems simplify the analysis of the EPR paradox.

Abstract

In this work we reexamine the EPR paradox for composite systems with a finite number of levels. The analysis emphasizes the connection between measurements and conditional probabilities. This connection implies that when a measurement is performed, the microscopic states compatible with the measurement is different from the class of all possible microscopic states, therefore the new quantum state and the probability distribution change and become a function of the observable being measured. Therefore, the predictions that one can make given the knowledge of the result of a measurement change. Systems with finitely many levels are simpler to describe because the analysis is not encumbered by the mathematical technicalities of the continuous case, the underlying physical interpretations are the same and the experimental setups used to test quantum mechanics with the paradox in mind finitely many levels.e same.