# A predictive solution of the EPR paradox

## TL;DR

This paper resolves the EPR paradox by demonstrating that quantum predictions and post-measurement states are consistent with the Heisenberg uncertainty principle, using two equivalent approaches.

## Contribution

It introduces two equivalent methods for analyzing the EPR paradox, confirming no violation of quantum principles occurs.

## Key findings

- No violation of the Heisenberg uncertainty principle occurs.
- Quantum conditional expectation aligns with von Neumann post-measurement state.
- The two approaches are mathematically equivalent.

## Abstract

In this work, we examine the paradox proposed by Einstein, Podolsky, and Rosen (EPR). They argued that since one may know the exact momentum of a particle without measurement and subsequently measure its position, a contradiction with the Heisenberg uncertainty principle arises. We demonstrate that there is no paradox by two equivalent approaches: first, by computing the quantum conditional expectation to make predictions after a measurement; and second, using the von Neumann post-measurement state. We establish the equivalence between these two methods. In both cases the predictor is an operator valued function of the observables being measured. This ensures that no violation of the Heisenberg uncertainty principle occurs.