A nice paper by Morrison demonstrates the recent convergence of opinion that has taken place concerning the graviton propagator on de Sitter background. We here discuss the few points which remain under dispute. First, the inevitable decay of tachyon
ic scalars really does result in their 2-point functions breaking de Sitter invariance. This is obscured by analytic continuation techniques which produce formal solutions to the propagator equation that are not propagators. Second, Morrisons de Sitter invariant solution for the spin two sector of the graviton propagator involves derivatives of the scalar propagator at $M^2 = 0$, where it is not meromorphic unless de Sitter breaking is permitted. Third, de Sitter breaking does not require zero modes. Fourth, the ambiguity Morrison claims in the equation for the spin two structure function is fixed by requiring it to derive from a mode sum. Fifth, Morrisons spin two sector is not physically equivalent to ours because their coincidence limits differ. Finally, it is only the noninvariant propagator that gets the time independence and scale invariance of the tensor power spectrum correctly.
We compute the linearized Weyl-Weyl correlator using a new solution for the graviton propagator on de Sitter background in de Donder gauge. The result agrees exactly with a previous computation in a noncovariant gauge. We also use dimensional regular
ization to compute the one loop expectation value of the square of the Weyl tensor.
We have theoretically and experimentally address the possible tandem electro-optical modulator configurations that can be employed to implement Frequency Coded Quantum Key Distribution systems (FC-QKD). A closed and general formulation of the end to
end field propagation in a dispersion compensated FC-QKD optical fiber system under the low modulation index regime is presented which accounts for all the possible tandem combinations. The properties and the parameter selection of the modulators to achieve each one are summarized. We also address which protocol (B92, BB84 or either) is feasible to be implemented with each configuration. The results confirm those reported for the configurations previously reported in the literature and, at the same time, show the existence of four novel tandem modulator configurations that can also be employed. We have also provided experimental evidence of the successful operation of the novel configurations that confirm the behavior predicted by the theoretical results.
