Decoherence induced by the noise of primordial graviton with minimum uncertainty initial states

We have investigated the decoherence induced by the primordial graviton, using the influence functional method, to show whether this method is still effective in detecting graviton if the initial state is not a Bunch–Davies vacuum but rather a minimum uncertainty state. This minimum uncertainty condition allows the initial state of the primordial graviton to be an entanglement state between the polarization or, more generally, a superposition state between a vacuum and that entanglement. Both of those states have a non-classical correlation between the two polarization modes. We found that this method is still effective for detecting gravitons if the density matrix of the initial state does not have non-diagonal elements, where the maximum decoherence time is about 20 s, and the dimensions of the interferometer could be reduced if the total graviton increases.