Complex Field Formulation of the Quantum Estimation Theory

Understand

We present a complex field formulation of the quantum estimation theory that works natively with complex statistics on the dependence of complex parameters.

• This formulation states new complex versions of the main quantities and results of the estimation theory depending on complex parameters, such as Fisher information matrices and Cram\'er-Rao bounds.
• This can be useful in contexts where the quantum states are described through complex parameters, such as coherent states or squeezed states.
• We show an example of an application of our theory in quantum communication with coherent states.