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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 forthese states, ESD never occurs. These states are generalizations of theso-called High NOON states, shown to decrease the Rayleigh limit of lambda tolambda/N, which promises great improvement in resolution of interferencepatterns if states with large N are physically realized. However, we show thatin dephasing NOON states, the time to reach V_crit, critical visibility, scalesinversely with N^2. On the practical level, this shows that as N increases, thevisibility degrades much faster, which is likely to be a considerable drawbackfor any practical application of these states.

Nonexistence of Entanglement Sudden Death in High NOON States