Testing the equivalence principle and discreteness of spacetime through the t3 gravitational phase with quantum information technology

Fabrizio Tamburini,Ignazio Licata

doi:10.1016/j.physletb.2020.135792

Fabrizio Tamburini, Ignazio Licata

Open Access

https://doi.org/10.1016/j.physletb.2020.135792

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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 [1–4] by revealing the gravitational t3 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 [5,6]. We find that this setup, built with massive mesoscopic particles, can potentially reveal the t3 gravitational phase term and thus, the BMV effect.

Highlights

Quantum Gravity (QG) can be at all effects considered the Holy Grail of modern physics
In this work we propose an ideal experiment based on quantum information technologies and entangled states to verify the principle of equivalence (PE) through the t3 phase factor according to Ref. [1,2,3,4] and discuss the detection of the shadowy signatures of the emergence of low-energy quantum gravity (LEQG) fluctuations
The detection of gravitational wave (GW) is one of the most important revolutions in modern multimessenger astronomy [39,40,41] and a challenging and outstanding test of Einstein’s General Relativity and the subject of current and next-generation experiments such as LIGO and VIRGO with the recent observations of GWs [42,43,44,45,46,47,48,49,50,51], experiments mainly based on classical interferometric techniques affected by the presence of photon shot noise [52] that can be reduced with techniques based on squeezed light [53]

Summary

GRAVITATIONAL FIELD FLUCTUATIONS AND THE EQUIVALENCE PRINCIPLE

The detection of general gravitational field perturbations, including those generated by LEQG, can proceed in a similar way as discussed in [5, 6], where the authors analyzed the problem of building of a quantum cryptographic key in a curved spacetime with entangled states. A deeper discussion about the coloring of the white noise representing the ideal cryptographic key due to the fluctuations of the gravitational field and the signal detection via the analysis of the stochastic noise is reported in the supplementary material As this effect is supposed to be detectable by using particles with masses of the order of a millionth of a Planck mass (10−14 kg) [1, 3, 4], only one neutron pair on a bunch of ∼ 106 neutrons would be able to give a signal to reveal the t3 phase factor. The experiment can be in principle feasible with current quantum information technologies

CONCLUSIONS

THE STOCHASTIC COLOR OF LEQG FLUCTUATIONS

SIGNAL DETECTION VIA STOCHASTIC NOISE ANALYSIS