Compensation of detection losses in quantum state reconstruction

Thomas Richter

Stefan Weigert

Th. Richter

We present a new and quite simple representation of the realistic pattern functions needed to reconstruct the density matrix in the Fock basis from quadrature distributions measured with non-ideal detectors. We show that they can be expressed as a finite weighted sum over the ideal pattern functions of scaled argument. Moreover we propose an algorithm which takes the detection loss-affected density matrix elements and produces the Wigner function (s-parametrized quasiprobability) of the signal field.

Konrad Banaszek

I present an iterative algorithm for reconstructing the Wigner function from homodyne statistics. The proposed method, based on maximum-likelihood estimation, is capable of compensating for detection losses in a numerically stable way.

Paolo Tombesi, David Vitali

T. Kiss, Ulrike Herzog, Ulf Leonhardt

The authors of the preceding Comment [G. M. D'Ariano and C. Macchiavello, preceding paper, Phys. Rev. A 57, 3131 (1998)] tried to reestablish a $0.5$ efficiency bound for loss compensation in optical homodyne tomography. In our reply we demonstrate that neither does such a rigorous bound exist nor is the bound required for ruling out the state reconstruction of an individual system [G. M. D'Ariano and H. P. Yuen, Phys. Rev. Lett. 76, 2832 (1996)].