Point Estimation of States of Finite Quantum Systems

Abstract

The estimation of the density matrix of a $k$-level quantum system is studied when the parametrization is given by the real and imaginary part of the entries and they are estimated by independent measurements. It is established that the properties of the estimation procedure depend very much on the invertibility of the true state. In particular, in case of a pure state the estimation is less efficient. Moreover, several estimation schemes are compared for the unknown state of a qubit when one copy is measured at a time. It is shown that the average mean quadratic error matrix is the smallest if the applied observables are complementary. The results are illustrated by computer simulations.

16 pages, 5 figures

References in corpus (7)

• State estimation for large ensembles
• Minimal qubit tomography
• Estimating the spectrum of a density operator
• Optimal full estimation of qubit mixed states
• Quantum tomography as normalization of incompatible observations
• Estimating mixed quantum states
• State tomography for two qubits using reduced densities

Cited by in corpus (5)

• Quantum Fisher information for density matrices with arbitrary ranks
• Optimal quantum-state tomography with known parameters
• Complementarity and the algebraic structure of 4-level quantum systems
• A quantum prediction as a collection of epistemically restricted classical predictions
• Sudden change of interferometric power for X shape states