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We study quantum stochastic trajectories of a field under quantum non-demolition measurement of its photon number using a scheme based on the optical Kerr effect. The signal field is shown to evolve into a state consisting of two Fock states (Fock state qubit) entangled with a probe, with the lifetime of such a state being much longer than the mean time between counts on the detectors. However, this pairwise state is not stable, excepting some particular cases, and it tends asymptotically with time to a pure Fock state.
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