Sampling the canonical phase from phase-space functions

We discuss the possibility of sampling exponential moments of the canonical phase from the s-parametrized phase space functions. We show that the sampling kernels exist and are well-behaved for any s>-1, whereas for s=-1 the kernels diverge in the origin. In spite of that we show that the phase space moments can be sampled with any predefined accuracy from the Q-function measured in the double-homodyne scheme with perfect detectors. We discuss the effect of imperfect detection and address sampling schemes using other measurable phase-space functions. Finally, we discuss the problem of sampling the canonical phase distribution itself.Comment: 10 pages, 7 figures, REVTe

Quantum inference of states and processes

The maximum-likelihood principle unifies inference of quantum states and processes from experimental noisy data. Particularly, a generic quantum process may be estimated simultaneously with unknown quantum probe states provided that measurements on probe and transformed probe states are available. Drawbacks of various approximate treatments are considered.Comment: 7 pages, 4 figure

Maximum likelihood estimation of photon number distribution from homodyne statistics

We present a method for reconstructing the photon number distribution from the homodyne statistics based on maximization of the likelihood function derived from the exact statistical description of a homodyne experiment. This method incorporates in a natural way the physical constraints on the reconstructed quantities, and the compensation for the nonunit detection efficiency.Comment: 3 pages REVTeX. Final version, to appear in Phys. Rev. A as a Brief Repor

Least-squares inversion for density-matrix reconstruction

We propose a method for reconstruction of the density matrix from measurable time-dependent (probability) distributions of physical quantities. The applicability of the method based on least-squares inversion is - compared with other methods - very universal. It can be used to reconstruct quantum states of various systems, such as harmonic and and anharmonic oscillators including molecular vibrations in vibronic transitions and damped motion. It also enables one to take into account various specific features of experiments, such as limited sets of data and data smearing owing to limited resolution. To illustrate the method, we consider a Morse oscillator and give a comparison with other state-reconstruction methods suggested recently.Comment: 16 pages, REVTeX, 6 PS figures include

Matter-wave entanglement and teleportation by molecular dissociation and collisions

We propose dissociation of cold diatomic molecules as a source of atom pairs with highly correlated (entangled) positions and momenta, approximating the original quantum state introduced by Einstein, Podolsky and Rosen (EPR) [Phys. Rev. 47, 777 (1935)]. Wavepacket teleportation is shown to be achievable by its collision with one of the EPR correlated atoms and manipulation of the other atom in the pair.Comment: REVTeX, 4 pages, 3 figures. Text reformulated, modified figs. 1 and 2. Accepted by Phys. Rev. Let

Direct sampling of exponential phase moments of smoothed Wigner functions

We investigate exponential phase moments of the s-parametrized quasidistributions (smoothed Wigner functions). We show that the knowledge of these moments as functions of s provides, together with photon-number statistics, a complete description of the quantum state. We demonstrate that the exponential phase moments can be directly sampled from the data recorded in balanced homodyne detection and we present simple expressions for the sampling kernels. The phase moments are Fourier coefficients of phase distributions obtained from the quasidistributions via integration over the radial variable in polar coordinates. We performed Monte Carlo simulations of the homodyne detection and we demonstrate the feasibility of direct sampling of the moments and subsequent reconstruction of the phase distribution.Comment: RevTeX, 8 pages, 6 figures, accepted Phys. Rev.

Braggoriton--Excitation in Photonic Crystal Infiltrated with Polarizable Medium

Light propagation in a photonic crystal infiltrated with polarizable molecules is considered. We demonstrate that the interplay between the spatial dispersion caused by Bragg diffraction and polaritonic frequency dispersion gives rise to novel propagating excitations, or braggoritons, with intragap frequencies. We derive the braggoriton dispersion relation and show that it is governed by two parameters, namely, the strength of light-matter interaction and detuning between the Bragg frequency and that of the infiltrated molecules. We also study defect-induced states when the photonic band gap is divided into two subgaps by the braggoritonic branches and find that each defect creates two intragap localized states inside each subgap.Comment: LaTeX, 8 pages, 5 figure

Continuous-variable optical quantum state tomography

This review covers latest developments in continuous-variable quantum-state tomography of optical fields and photons, placing a special accent on its practical aspects and applications in quantum information technology. Optical homodyne tomography is reviewed as a method of reconstructing the state of light in a given optical mode. A range of relevant practical topics are discussed, such as state-reconstruction algorithms (with emphasis on the maximum-likelihood technique), the technology of time-domain homodyne detection, mode matching issues, and engineering of complex quantum states of light. The paper also surveys quantum-state tomography for the transverse spatial state (spatial mode) of the field in the special case of fields containing precisely one photon.Comment: Finally, a revision! Comments to lvov(at)ucalgary.ca and raymer(at)uoregon.edu are welcom

The characterization of Gaussian operations and Distillation of Gaussian States

We characterize the class of all physical operations that transform Gaussian states to Gaussian states. We show that this class coincides with that of all operations which can be performed on Gaussian states using linear optical elements and homodyne measurements. For bipartite systems we characterize the processes which can be implemented by local operations and classical communication, as well as those that can be implemented using positive partial transpose preserving maps. As an application, we show that Gaussian states cannot be distilled by local Gaussian operations and classical communication. We also define and characterize positive (but not completely positive) Gaussian maps.Comment: 8 pages, revtex4; v4: published version; v3: more details on V(gamma), some typos corrected, formulations clarifie

Non-classical correlations from dissociation time entanglement

We discuss a strongly entangled two-particle state of motion that emerges naturally from the double-pulse dissociation of a diatomic molecule. This state, which may be called dissociation-time entangled, permits the unambiguous demonstration of non-classical correlations by violating a Bell inequality based on switched single particle interferometry and only position measurements. We apply time-dependent scattering theory to determine the detrimental effect of dispersion. The proposed setup brings into reach the possibility of establishing non-classical correlations with respect to system properties that are truly macroscopically distinct.Comment: 8 pages, 2 figures; corresponds to published versio