2006/10/16 by D. Petz, D Petz, K. M. Hangos +3 · 1 citation
Computer Science · Physics and Astronomy · #Density matrix #Matrix (chemical analysis) #Parametrization (atmospheric modeling) #Quadratic equation #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum many-body systems #Quantum phase estimation algorithm #Quantum system #Qubit #State (computer science) #quant-ph
paper · pdf · doi:10.1088/1751-8113/40/28/s06
16 pages, 5 figures
arxiv created 2006/10/16 · openalex publication_date 2007/06/27 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 the case of a pure state, the estimation should be constrained to ensure the positive definiteness of the estimate. An efficient constraining algorithm is proposed and it yields an asymptotically unbiased estimate. 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. All the results are illustrated by computer simulations.