Eur. Phys. J. D 40, 139-146 (2006)
https://doi.org/10.1140/epjd/e2006-00129-8

Quantum state reconstruction by entangled measurements

Dipartimento di Fisica dell'Università degli Studi di Milano, via Celoria 16, 20133 Milano, Italy

Corresponding author: ^a matteo.paris@fisica.unimi.it

Received: 13 February 2006
Revised: 20 April 2006
Published online: 15 June 2006

Abstract

We address quantum state reconstruction for d-dimensional systems based on measuring, on the system of interest and a probe, of a single entangled observable defined on the bipartite system/probe Hilbert space. We show that the statistics of the measurement and the knowledge of the probe preparation suffice to reliably reconstruct the density matrix of the system, as well as the expectation value of any desired operator, including those not corresponding to observable quantities. The statistical robustness of the reconstruction is examined and a method is developed to minimize statistical errors by tuning the probe preparation. Numerical simulations of the whole reconstruction procedure are also presented for qubit systems.