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In this paper, we propose two protocols for generating super-resolving single-photon (SRSP) number-path-entangled states from general maximally number-path-entangled NOON states. It is our purpose to show that, contrary to popular belief, a field in a single-photon state can carry multifold phase information. We also show that both protocols generate the desired state with different probabilities depending on the type of detectors being used. Such SRSP number-path-entangled states preserve high resolving power but lack the requirement of a multiphoton absorbing resist, which may serve as a proof-of-principle prototype for quantum lithography in the future. [ABSTRACT FROM AUTHOR]

We study effects of phase fluctuations on phase sensitivity and visibility of a class of robust path-entangled photon Fock states (known as mm' states) as compared to the maximally path-entangled NOON states in the presence of realistic phase fluctuations such as turbulence noise. Our results demonstrate that the mm' states, which are more robust than the NOON state against photon loss, perform equally well when subject to such fluctuations. We derive the quantum Fisher information with the phase-fluctuation noise and show that the phase sensitivity with parity detection for both of the above states saturates the quantum Cramér-Rao bound in the presence of such noise, suggesting that parity detection is an optimal detection strategy. [ABSTRACT FROM AUTHOR]