We study the dynamics of entanglement in continuous variable quantum systems. 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 circumstances, ESD never occurs. These states are generalizations of the so-called high NOON states (i.e., a superposition of N photons in the first mode, O in the second, with O photons in the first, N in the second), shown to decrease the Rayleigh limit of λ to , which promises great improvement in resolution of interference patterns if states with large N are physically realized [Phys. Rev. Lett. 85, 2733 (2000) ]. However, we show that in dephasing NOON states, the time to reach some critical visibility , scales inversely with . 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.
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