Testing the equivalence principle and discreteness of spacetime through the $t^3$ gravitational phase with quantum information technology

TL;DR

This paper proposes a quantum information-based experiment to detect quantum gravitational effects, specifically the $t^3$ phase term, by analyzing noise in entangled particle measurements to test the equivalence principle and spacetime discreteness.

Contribution

It introduces a novel method using quantum cryptography techniques to measure gravitational field fluctuations and detect the $t^3$ phase, advancing experimental quantum gravity research.

Findings

Potential to detect the $t^3$ gravitational phase term.

Method to analyze gravitational fluctuations via noise coloring.

Proposal to use mesoscopic particles for sensitivity enhancement.

Abstract

We propose a new thought experiment, based on present-day Quantum Information Technologies, to measure quantum gravitational effects through the Bose-Marletto-Vedral (BMV) effect by revealing the gravitational $t^3$ phase term, its expected relationships with low-energy quantum gravity phenomena and test the equivalence principle of general relativity. The technique here proposed promise to reveal gravitational field fluctuations from the analysis of the stochastic noise associated to an ideal output of a measurement process of a quantum system. To improve the sensitivity we propose to cumulate the effects of the gravitational field fluctuations in time on the outputs of a series of independent measurements acted on entangled states of particles, like in the building of a quantum cryptographic key, and extract from the associated time series the effect of the expected gravitational field fluctuations. In fact, an ideal quantum cryptographic key, built with the sharing of maximally entangled states of particles, is represented by a random sequence of uncorrelated symbols mathematically described by a perfect white noise, a stochastic process with zero mean and without correlation between its values taken at different times. Gravitational field perturbations, including quantum gravity fluctuations and gravitational waves, introduce additional phase terms that decohere the entangled pairs used to build the quantum cryptographic key, with the result of coloring the white noise. We find that this setup, built with massive mesoscopic particles, can potentially reveal the $t^3$ gravitational phase term and thus, the BMV effect.