Quantum estimation via minimum Kullback entropy principle

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.

7 pages, slightly revised version, no figures

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• About the probability distribution of a quantity with given mean and variance
• Periodic orbits in deterministic discrete-time evolutionary game dynamics: An information-theoretic perspective
• Exact and approximate solutions for the quantum minimum-Kullback-entropy estimation problem
• Assessing thermalization and estimating the Hamiltonian with output data only
• The initial system-bath state via the maximum-entropy principle
• Prior-Aware Distribution Estimation for Differential Privacy
• Minimum Relative Entropy for Quantum Estimation: Feasibility and General Solution
• Reconstructing the relaxation dynamics induced by an unknown heat bath