Quantum metrology and quantum information necessitate a profound study of suitable states. Attenuations induced by free-space communication links or fluctuations in the generation of such states limit the quantum enhancement in possible applications. For this reason we investigate quantum features of mixtures of so-called NOON states propagating in atmospheric channels. First, we show that noisy NOON states can still yield a phase resolution beyond classical limitations. Second, we identify entanglement of noisy NOON states after propagation in fluctuating loss channels. To do so, we apply the partial transposition criterion. Our theoretical analysis formulates explicit bounds which are indispensable for experimental verification of quantum entanglement and applications in quantum metrology.

• Received 10 December 2014
• Revised 27 January 2015

DOI:https://doi.org/10.1103/PhysRevA.91.042332