# Quantum predictions for an unmeasured system cannot be simulated with a finite-memory classical system

## TL;DR

This paper demonstrates that simulating the quantum correlations of an unmeasured, entangled system with a finite-memory classical model is impossible, requiring infinite memory and communication, thus highlighting fundamental nonlocality.

## Contribution

It introduces a thermodynamical argument showing that finite-memory classical models cannot replicate quantum predictions for an entangled system undergoing sequential measurements.

## Key findings

- Finite-memory classical models cannot simulate quantum correlations.
- Simulating quantum predictions requires infinite memory and communication.
- Thermodynamical considerations predict heating if classical models are finite-memory.

## Abstract

We consider an ideal experiment in which unlimited nonprojective quantum measurements are sequentially performed on a system that is initially entangled with a distant one. At each step of the sequence, the measurements are randomly chosen between two. However, regardless of which measurement is chosen or which outcome is obtained, the quantum state of the pair always remains entangled. We show that the classical simulation of the reduced state of the distant system requires not only unlimited rounds of communication, but also that the distant system has infinite memory. Otherwise, a thermodynamical argument predicts heating at a distance. Our proposal can be used for experimentally ruling out nonlocal finite-memory classical models of quantum theory.