Quorum of observables for universal quantum estimation

Any method for estimating the ensemble average of arbitrary operator (observables or not, including the density matrix) relates the quantity of interest to a complete set of observables, i.e. a quorum}. This corresponds to an expansion on an irreducible set of operators in the Liouville space. We give two general characterizations of these sets. All the known unbiased reconstruction techniques, i.e. ``quantum tomographies'', can be described in this framework. New operatorial resolutions are given that can be used to implement novel reconstruction schemes.Comment: Latex, no figure

Quantum Tomography

This is the draft version of a review paper which is going to appear in "Advances in Imaging and Electron Physics"Comment: To appear in "Advances in Imaging and Electron Physics". Some figs with low resolutio

Quantum Tomography of a system of three-level atoms

We analyze the possibility of tomographic reconstruction of a system of three-level atoms in both non-degenerate and degenerate cases. In the non-degenerate case (when both transitions can be accessed independently) a complete reconstruction is possible. In the degenerate case (when both transitions are excited simultaneously) the complete reconstruction is achievable only for a single atom in the Sigma configuration. For multiple Sigma atoms, or even a single atom in the Lambda configuration, only partial reconstruction is possible. Examples of one and two-atom cases are explicitly considered.Comment: accepted in J.Phys.A: Math.& Theo

To take a (binary) decision you'd better use entanglement

We address two-mode quantum interferometry as binary measurements aimed at determining whether or not a phase perturbation has occurred. We show that optimized measurements achieve the best sensitivity when the input state is entangled. A concrete set-up based on parametric sources of entanglement and photodetection is also suggested and shown to approach ideal sensitivity

Comment on ``Creating Metastable Schroedinger Cat States''

After a careful analysis of the feedback model recently proposed by Slosser and Milburn [Phys. Rev. Lett. 75, 418 (1995)], we are led to the conclusion that---under realistic conditions---their scheme is not significantly more effective in the production of linear superpositions of macroscopically distinguishable quantum states than the usual quantum-optical Kerr effect.Comment: 1 page, RevTeX, 1 eps figure (fig_1.eps), accepted for publication in Physical Review Letters [Phys. Rev. Lett. 77 (9) (1996)

Using entanglement improves precision of quantum measurements

We show how entanglement can be used to improve the estimation of an unknown transformation. Using entanglement is always of benefit, in improving either the precision or the stability of the measurement. Examples relevant for applications are illustrated, for either qubits and continuous variable

Optimal phase estimation in quantum networks

We address the problem of estimating the phase phi given N copies of the phase rotation u(phi) within an array of quantum operations in finite dimensions. We first consider the special case where the array consists of an arbitrary input state followed by any arrangement of the N phase rotations, and ending with a POVM. We optimise the POVM for a given input state and fixed arrangement. Then we also optimise the input state for some specific cost functions. In all cases, the optimal POVM is equivalent to a quantum Fourier transform in an appropriate basis. Examples and applications are given.Comment: 9 pages, 2 figures; this is an extended version of arXiv:quant-ph/0609160. v2: minor corrections in reference