Fundamental quantum limits in optical metrology from rate-distortion theory

Understand

We derive fundamental lower bounds on the performance of optical metrology and communication systems in a Bayesian framework.

• The derivation uses classical rate-distortion theory in conjunction with bounds on the capacity to transmit classical information of various optical channels specified by the system design.
• The bounds are expressed in terms of the system parameters, the prior probability distribution of the parameter, and the average energy, i.e., number of photons $E$ in the probe state.
• For phase estimation, the bounds pertain to a cyclic mean squared error criterion incorporating the cyclic nature of the phase.