  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.
