Abstract
We consider the problem of estimating an unknown but constant carrier phase modulation using a general, possibly entangled, -mode optical probe through independent and identical uses of a lossy bosonic channel with additive thermal noise. We find an upper bound to the quantum Fisher information (QFI) of estimating as a function of , the mean and variance of the total number of photons in the -mode probe, the transmissivity , and mean thermal photon number per mode of the bosonic channel. Since the inverse of QFI provides a lower bound to the mean-square error (MSE) of an unbiased estimator of , our upper bound to the QFI provides a lower bound to the MSE. It already has found use in proving fundamental limits of covert sensing and could find other applications requiring bounding the fundamental limits of sensing an unknown parameter embedded in a correlated field.
- Received 2 October 2017
DOI:https://doi.org/10.1103/PhysRevA.96.062306
©2017 American Physical Society