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Abstract: The lossy propagation law generalization of Lambert-Beer-s law for classicalradiation loss for non-classical, dual-mode entangled states is derived fromfirst principles, using an infinite-series of beam splitters to modelcontinuous photon loss. This model is general enough to accommodatestray-photon noise along the propagation, as well as amplitude attenuation. Anexplicit analytical expression for the density matrix as a function ofpropagation distance is obtained for completely general input states withbounded photon number in each mode. The result is analyzed numerically forvarious examples of input states. For N00N state input, the loss of coherenceand entanglement is super exponential as predicted by a number of previousstudies. However, for generic input states, where the coefficients aregenerated randomly, the decay of coherence is very different; in fact no worsethan the classical Beer-Lambert law. More surprisingly, there is a plateu at amid-range interval in propagation distance where the loss is in factsub-classical, following which it resumes the classical rate. The qualitativebehavior of the decay of entanglement for two-mode propagation is also analyzednumerically for ensembles of random states using the behavior of negativity asa function of propagation distance.



Autor: Ulvi Yurtsever

Fuente: https://arxiv.org/



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