  The weak nonlinear Kerr interaction between single photons and intense laser
fields has been recently proposed as a basis for distributed optics-based
solutions to few-qubit applications in quantum communication and computation.
Here, we analyze the above Kerr interaction by employing a continuous-time
multi-mode model for the input/output fields to/from the nonlinear medium. In
contrast to previous single-mode treatments of this problem, our analysis takes
into account the full temporal content of the free-field input beams as well as
the non-instantaneous response of the medium. The main implication of this
model, in which the cross-Kerr phase shift on one input is proportional to the
photon flux of the other input, is the existence of phase noise terms at the
output. We show that these phase noise terms will preclude satisfactory
performance of the parity gate proposed by Munro, Nemoto, and Spiller [New J.
Phys. 7, 137 (2005)].
