Quantum Enhanced Classical Sensor Networks

The quantum enhanced classical sensor network consists of $K$ clusters of $N_e$ entangled quantum states that have been trialled $r$ times, each feeding into a classical estimation process. Previous literature has shown that each cluster can {ideally} achieve an estimation variance of $1/N_e^2r$ for sufficient $r$. We begin by deriving the optimal values for the minimum mean squared error of this quantum enhanced classical system. We then show that if noise is \emph{absent} in the classical estimation process, the mean estimation error will decay like $\Omega(1/KN_e^2r)$. However, when noise is \emph{present} we find that the mean estimation error will decay like $\Omega(1/K)$, so that \emph{all} the sensing gains obtained from the individual quantum clusters will be lost.