Biased tomography schemes: an objective approach.

We report on an intrinsic relationship between the maximum-likelihood quantum-state estimation and the representation of the signal. A quantum analogy of the transfer function determines the space where the reconstruction should be done without the need for any ad hoc truncations of the Hilbert space. An illustration of this method is provided by a simple yet practically important tomography of an optical signal registered by realistic binary detectors.

[1]  A. I. Lvovsky,et al.  Iterative maximum-likelihood reconstruction in quantum homodyne tomography , 2003, quant-ph/0311097.

[2]  Dmitri Mogilevtsev,et al.  Diagonal element inference by direct detection , 1998 .

[3]  Royer Measurement of the Wigner function. , 1985, Physical review letters.

[4]  J. Peřina,et al.  Quantum state inference from photocount statistics: one-probe reconstruction and reconstruction checking the presence or absence of photons , 1998 .

[5]  Kevin Cahill,et al.  Ordered Expansions in Boson Amplitude Operators , 1969 .

[6]  Kevin Cahill,et al.  DENSITY OPERATORS AND QUASIPROBABILITY DISTRIBUTIONS. , 1969 .

[7]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[8]  Knight,et al.  Series representation of quantum-field quasiprobabilities. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[9]  Quantum homodyne tomography with a priori constraints , 1999, quant-ph/9901064.

[10]  J. Rehacek,et al.  Multiple-photon resolving fiber-loop detector , 2003 .

[11]  Banaszek,et al.  Direct probing of quantum phase space by photon counting. , 1996, Physical review letters.

[12]  L. Mandel,et al.  Optical Coherence and Quantum Optics , 1995 .

[13]  Vogel,et al.  Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase. , 1989, Physical review. A, General physics.

[14]  Marco Genovese,et al.  Experimental reconstruction of photon statistics without photon counting. , 2005, Physical review letters.

[15]  K. Banaszek,et al.  Direct measurement of the Wigner function by photon counting , 1999 .

[16]  Vogel,et al.  Unbalanced homodyning for quantum state measurements. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[17]  Y. Vardi,et al.  From image deblurring to optimal investments : maximum likelihood solutions for positive linear inverse problems , 1993 .