Complex Field Formulation of the Quantum Estimation Theory

Abstract

We present a complex field formulation of the quantum Fisher estimation theory that works natively with complex statistics on the dependence of complex parameters. This states new complex versions of the main quantities and results of the estimation theory depending on complex parameters, such as Fisher information matrices and Cramér-Rao bounds. This can be useful in contexts where the quantum states are described through complex parameters, as coherent states or squeezed states. We show an application of our theory in quantum communication with coherent states.

Stochastic optimization algorithms for quantum applications

“…In the case that the optimization space is the set of pure quantum states, the metric G can be chosen proportional to the quantum Fisher complex information matrix [101], that is,…”

Stochastic optimization algorithms for quantum applications

“…In the case of pure quantum states, we choose the metric G given by a quarter of the complex Quantum Fisher Information matrix [101], that is,…”