# Quantum to classical transition induced by gravitational time dilation

## TL;DR

This paper investigates how gravitational time dilation causes the loss of quantum coherence in Schrödinger cat states, analyzing various nonclassicality indicators and comparing gravitational effects to classical noise-induced decoherence.

## Contribution

It provides a comprehensive comparison of multiple nonclassicality indicators and highlights their dependence on the size of the quantum superposition, offering insights into gravitationally induced decoherence.

## Key findings

- Only two indicators depend critically on the size of the superposition
- Gravitational decoherence times are comparable to classical noise decoherence times
- Experimental observation of gravitational decoherence requires controlling classical noise levels

## Abstract

We study the loss of quantumness caused by time dilation [1] for a Schr\"odinger cat state. We give a holistic view of the quantum to classical transition by comparing the dynamics of several nonclassicality indicators, such as the Wigner function interference fringe, the negativity of the Wigner function, the nonclassical depth, the Vogel criterion and the Klyshko criterion. Our results show that only two of these indicators depend critically on the size of the cat, namely on how macroscopic the superposition is. Finally we compare the gravitation-induced decoherence times to the typical decoherence times due to classical noise originating from the unavoidable statistical fluctuations in the characteristic parameters of the system [21]. We show that the experimental observation of decoherence due to time dilation imposes severe limitations on the allowed levels of classical noise in the experiments.