  We study the dynamics of entanglement in continuous variable quantum systems
(CVQS). Specifically, we study the phenomena of Entanglement Sudden Death (ESD)
in general two-mode-N-photon states undergoing pure dephasing. We show that for
these states, ESD never occurs. These states are generalizations of the
so-called High NOON states, shown to decrease the Rayleigh limit of lambda to
lambda/N, which promises great improvement in resolution of interference
patterns if states with large N are physically realized. However, we show that
in dephasing NOON states, the time to reach V_crit, critical visibility, scales
inversely with N^2. On the practical level, this shows that as N increases, the
visibility degrades much faster, which is likely to be a considerable drawback
for any practical application of these states.
