  A framework is established for evaluating {\sc cphase} gates that use
single-photon cross-phase modulation (XPM) originating from the Kerr
nonlinearity. Prior work Phys. Rev. A {\bf 73,} 062305 (2006)], which assumed
that the control and target pulses propagated at the same group velocity,
showed that the causality-induced phase noise required by a non-instantaneous
XPM response function precluded the possibility of high-fidelity $\pi$-radian
conditional phase shifts. The framework presented herein incorporates the more
realistic case of group-velocity disparity between the control and target
pulses, as employed in existing XPM-based fiber-optical switches. Nevertheless,
the causality-induced phase noise identified in [Phys. Rev. A {\bf 73,} 062305
(2006)] still rules out high-fidelity $\pi$-radian conditional phase shifts.
This is shown to be so for both a reasonable theoretical model for the XPM
response function and for the experimentally-measured XPM response function of
silica-core fiber.
