Precision bounds for noisy nonlinear quantum metrology
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We derive the ultimate bounds on the performance of nonlinear measurement schemes in the presence of noise. In particular, we investigate the precision of the second-order estimation scheme in the presence of the two most detrimental types of noise, photon loss and phase diffusion. We find that the second-order estimation scheme is affected by both types of noise in an analogous way as the linear one. Moreover, we observe that for both types of noise the gain in the phase sensitivity with respect to the linear estimation scheme is given by a multiplicative term O(1/N). Interestingly, we also find that under certain circumstances, a careful engineering of the environment can, in principle, improve the performance of measurement schemes affected by phase diffusion.
Physical Review A (Atomic, Molecular and Optical Physics)
© 2014 American Physical Society. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher. Please refer to the journal's website for access to the definitive, published version.
Quantum Information, Computation and Communication