Enhancing axial localization with wavefront control.

Enhancing the ability to resolve axial details is crucial in three-dimensional optical imaging. We provide experimental evidence showcasing the ultimate precision achievable in axial localization using vortex beams. For Laguerre-Gauss (LG) beams, this remarkable limit can be attained with just a single intensity scan.

Intensity-Based Axial Localization at the Quantum Limit.

We derive fundamental precision bounds for single-point axial localization. For Gaussian beams, this ultimate limit can be achieved with a single intensity scan, provided the camera is placed at one of two optimal transverse detection planes. Hence, for axial localization there is no need of more complicated detection schemes.

Reading out Fisher information from the zeros of the point spread function.

We show that, for optical systems whose point spread functions exhibit isolated zeros, the information one can gain about the separation between two incoherent point light sources does not scale quadratically with the separation (which is the distinctive dependence causing Rayleigh's curse) but only linearly. Moreover, the dominant contribution to the separation information comes from regions in the vicinity of these zeros. We experimentally confirm this idea, demonstrating significant superresolution using natural or artificially created spectral doublets.

Adaptive Compressive Tomography with No a priori Information.

Quantum state tomography is both a crucial component in the field of quantum information and computation and a formidable task that requires an incogitable number of measurement configurations as the system dimension grows. We propose and experimentally carry out an intuitive adaptive compressive tomography scheme, inspired by the traditional compressed-sensing protocol in signal recovery, that tremendously reduces the number of configurations needed to uniquely reconstruct any given quantum state without any additional a priori assumption whatsoever (such as rank information, purity, etc.) about the state, apart from its dimension.

Quantum-Limited Time-Frequency Estimation through Mode-Selective Photon Measurement.

By projecting onto complex optical mode profiles, it is possible to estimate arbitrarily small separations between objects with quantum-limited precision, free of uncertainty arising from overlapping intensity profiles. Here we extend these techniques to the time-frequency domain using mode-selective sum-frequency generation with shaped ultrafast pulses. We experimentally resolve temporal and spectral separations between incoherent mixtures of single-photon level signals ten times smaller than their optical bandwidths with a tenfold improvement in precision over the intensity-only Cramér-Rao bound.

Unraveling beam self-healing.

We show that, contrary to popular belief, diffraction-free beams may not only reconstruct themselves after hitting an opaque obstacle but also, for example, Gaussian beams. We unravel the mathematics and the physics underlying the self-reconstruction mechanism and we provide for a novel definition for the minimum reconstruction distance beyond geometric optics, which is in principle applicable to any optical beam that admits an angular spectrum representation. Moreover, we propose to quantify the self-reconstruction ability of a beam via a newly established degree of self-healing.

Optimal measurements for resolution beyond the Rayleigh limit.

We establish the conditions to attain the ultimate resolution predicted by quantum estimation theory for the case of two incoherent point sources using a linear imaging system. The solution is closely related to the spatial symmetries of the detection scheme. In particular, for real symmetric point spread functions, any complete set of projections with definite parity achieves the goal.

Crystallizing highly-likely subspaces that contain an unknown quantum state of light.

In continuous-variable tomography, with finite data and limited computation resources, reconstruction of a quantum state of light is performed on a finite-dimensional subspace. In principle, the data themselves encode all information about the relevant subspace that physically contains the state. We provide a straightforward and numerically feasible procedure to uniquely determine the appropriate reconstruction subspace by extracting this information directly from the data for any given unknown quantum state of light and measurement scheme.

Evading Vacuum Noise: Wigner Projections or Husimi Samples?

The accuracy in determining the quantum state of a system depends on the type of measurement performed. Homodyne and heterodyne detection are the two main schemes in continuous-variable quantum information. The former leads to a direct reconstruction of the Wigner function of the state, whereas the latter samples its Husimi Q function.

Local Sampling of the Wigner Function at Telecom Wavelength with Loss-Tolerant Detection of Photon Statistics.

We report the experimental point-by-point sampling of the Wigner function for nonclassical states created in an ultrafast pulsed type-II parametric down-conversion source. We use a loss-tolerant time-multiplexed detector based on a fiber-optical setup and a pair of photon-number-resolving avalanche photodiodes. By capitalizing on an expedient data-pattern tomography, we assess the properties of the light states with outstanding accuracy.

Surmounting intrinsic quantum-measurement uncertainties in Gaussian-state tomography with quadrature squeezing.

We reveal that quadrature squeezing can result in significantly better quantum-estimation performance with quantum heterodyne detection (of H. P. Yuen and J.

Wavefront sensing reveals optical coherence.

Wavefront sensing is a set of techniques providing efficient means to ascertain the shape of an optical wavefront or its deviation from an ideal reference. Owing to its wide dynamical range and high optical efficiency, the Shack-Hartmann wavefront sensor is nowadays the most widely used of these sensors. Here we show that it actually performs a simultaneous measurement of position and angular spectrum of the incident radiation and, therefore, when combined with tomographic techniques previously developed for quantum information processing, the Shack-Hartmann wavefront sensor can be instrumental in reconstructing the complete coherence properties of the signal.

Cross-validated tomography.

We show that the information collected in the course of a generic quantum tomography experiment can be used for verifying experimenters' assumptions about the state preparation and measurement. In particular, systematic errors, such as drifts and instabilities inherent in the tomography setup, can be identified without the need for any specific measurements designed to detect such problems. This is done by statistical analysis of available tomography data.

Quantum-state reconstruction by maximizing likelihood and entropy.

Quantum-state reconstruction on a finite number of copies of a quantum system with informationally incomplete measurements, as a rule, does not yield a unique result. We derive a reconstruction scheme where both the likelihood and the von Neumann entropy functionals are maximized in order to systematically select the most-likely estimator with the largest entropy, that is, the least-bias estimator, consistent with a given set of measurement data. This is equivalent to the joint consideration of our partial knowledge and ignorance about the ensemble to reconstruct its identity.

Operational tomography: fitting of data patterns.

We build an operational scheme for the quantum state reconstruction based on the fitting of data patterns. Each data pattern corresponds to the response of the measurement setup to a predefined reference state. The set of data patterns can be measured experimentally in the calibration stage preceding to the reconstruction.

Quantum reconstruction of the mutual coherence function.

Light is a major carrier of information about the world around us, from the microcosmos to the macrocosmos. The present methods of detection are sensitive both to robust features, such as intensity, or polarization, and to more subtle effects, such as correlations. Here we show how wave front detection, which allows for registering the direction of the incoming wave flux at a given position, can be used to reconstruct the mutual coherence function when combined with some techniques previously developed for quantum information processing.

Nondiffracting beams for vortex tomography.

We propose a reconstruction of vortex beams based on implementation of quadratic transformations in the orbital angular momentum. The information is encoded in a superposition of Bessel-like nondiffracting beams. The measurement of the angular probability distribution at different positions allows for the reconstruction of the Wigner function.

Full tomography from compatible measurements.

We put forward a reconstruction scheme prompted by the relation between a von Neumann measurement and the corresponding informationally complete measurement induced in a relevant reconstruction subspace. This method is especially suited for the full tomography of complex quantum systems, where the intricacies of the detection part of the experiment can be greatly reduced provided some prior information is available. In broader terms this shows the importance of prior information in quantum theory.

Minimum uncertainty measurements of angle and angular momentum.

We present an accurate description of the conjugate pair angle-angular momentum in terms of the exponential of the angle instead of the angle itself, which leads to dispersion as a natural measure of resolution. Intelligent states minimizing the uncertainty product under the constraint of a given uncertainty in angle or in angular momentum turn out to be given by Mathieu wave functions. We discuss Gaussian approximations to these optimal states in terms of von Mises distributions.

Seasonal variations in detecting Borrelia burgdorferi sensu lato in rodents from north eastern Austria.

Austria is well known as an endemic area of Lyme borreliosis. To assess the annual variation of rodent populations that may host agents of Lyme borreliosis we collected rodents in northeastern Austria. Life traps were set out every six weeks during a year consecutively in one each of the three different zones (Hohenau, Ernstbrunn, Vienna Woods) that cover the main habitat characteristics of small mammals in northeastern Austria.

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.

Triggered qutrits for quantum communication protocols.

A general protocol in quantum information and communication relies in the ability of producing, transmitting, and reconstructing, in general, qunits. In this Letter we show for the first time the experimental implementation of these three basic steps on a pure state in a three-dimensional space, by means of the orbital angular momentum of the photons. The reconstruction of the qutrit is performed with tomographic techniques and a maximum-likelihood estimation method.