Quantum estimation via minimum Kullback entropy principle

TL;DR

This paper introduces a quantum state estimation method based on minimizing the quantum relative entropy with incomplete measurement data and prior information, applicable to single observable measurements and weak Hamiltonian processes.

Contribution

It develops a minimum Kullback entropy principle for quantum estimation, extending to cases with incomplete data and prior knowledge, and demonstrates its application to qubits and harmonic oscillators.

Findings

Effective estimation from single observable data

Application to weak Hamiltonian process estimation

Analysis of qubit and harmonic oscillator systems

Abstract

We address quantum estimation in situations where one has at disposal data from the measurement of an incomplete set of observables and some a priori information on the state itself. By expressing the a priori information in terms of a bias toward a given state the problem may be faced by minimizing the quantum relative entropy (Kullback entropy) with the constraint of reproducing the data. We exploit the resulting minimum Kullback entropy principle for the estimation of a quantum state from the measurement of a single observable, either from the sole mean value or from the complete probability distribution, and apply it as a tool for the estimation of weak Hamiltonian processes. Qubit and harmonic oscillator systems are analyzed in some details.