Intensity correlations in the Wigner representation.

We derive a compact expression for the second-order correlation function [Formula: see text] of a quantum state in terms of its Wigner function, thereby establishing a direct link between [Formula: see text] and the state's shape in phase space. We conduct an experiment that simultaneously measures [Formula: see text] through direct photocounting and reconstructs the Wigner function via homodyne tomography. The results confirm our theoretical predictions.

An operational distinction between quantum entanglement and classical non-separability.

Quantum entanglement describes superposition states in multi-dimensional systems-at least two partite-which cannot be factorized and are thus non-separable. Non-separable states also exist in classical theories involving vector spaces. In both cases, it is possible to violate a Bell-like inequality.

Polarization squeezing in chalcogenide fibers.

We experimentally demonstrate the generation of polarization-squeezed light in a short piece of solid-core chalcogenide (ChG) (AsS) fiber via the Kerr effect for femtosecond pulses at 1.56 µm. Directly measured squeezing of -2.

Evidence-Based Certification of Quantum Dimensions.

Identifying a reasonably small Hilbert space that completely describes an unknown quantum state is crucial for efficient quantum information processing. We introduce a general dimension-certification protocol for both discrete and continuous variables that is fully evidence based, relying solely on the experimental data collected and no other unjustified assumptions whatsoever. Using the Bayesian concept of relative belief, we take the effective dimension of the state as the smallest one such that the posterior probability is larger than the prior, as dictated by the data.

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.

Efficient line shape estimation by ghost spectroscopy.

Recovering the original spectral line shapes from data obtained by instruments with extended transmission profiles is a basic tenet in spectroscopy. By using the moments of the measured lines as basic variables, we turn the problem into a linear inversion. However, when only a finite number of these moments are relevant, the rest of them act as nuisance parameters.

Quantum-enhanced interferometer using Kerr squeezing.

One of the prime applications of squeezed light is enhancing the sensitivity of an interferometer below the quantum shot-noise limit, but so far, no such experimental demonstration was reported when using the optical Kerr effect. In prior setups involving Kerr-squeezed light, the role of the interferometer was merely to characterize the noise pattern. The lack of such a demonstration was largely due to the cumbersome tilting of the squeezed ellipse in phase space.

Optimizing the generation of polarization squeezed light in nonlinear optical fibers driven by femtosecond pulses.

Bright squeezed light can be generated in optical fibers utilizing the Kerr effect for ultrashort laser pulses. However, pulse propagation in a fiber is subject to nonconservative effects that deteriorate the squeezing. Here, we analyze two-mode polarization squeezing, which is SU(2)-invariant, robust against technical perturbations, and can be generated in a polarization-maintaining fiber.

Anticaustics in a Fabry-Perot interferometer.

We address the response of a Fabry-Perot interferometer to a monochromatic point source. We calculate the anticaustics (that is, the virtual wavefronts of null path difference) resulting from the successive internal reflections occurring in the system. They turn out to be a family of ellipsoids (or hyperboloids) of revolution, which allows us to reinterpret the operation of the Fabry-Perot interferometer from a geometrical point of view that facilitates comparison with other apparently disparate arrangements, such as Young's double slit.

From polarization multipoles to higher-order coherences.

We demonstrate that the multipoles associated with the density matrix are truly observable quantities that can be unambiguously determined from intensity moments. Given their correct transformation properties, these multipoles are the natural variables to deal with a number of problems in the quantum domain. In the case of polarization, the moments are measured after the light has passed through two quarter-wave plates, one half-wave plate, and a polarizing beam splitter for specific values of the angles of the wave plates.

Intrinsic Sensitivity Limits for Multiparameter Quantum Metrology.

The quantum Cramér-Rao bound is a cornerstone of modern quantum metrology, as it provides the ultimate precision in parameter estimation. In the multiparameter scenario, this bound becomes a matrix inequality, which can be cast to a scalar form with a properly chosen weight matrix. Multiparameter estimation thus elicits trade-offs in the precision with which each parameter can be estimated.

Fundamental quantum limits in ellipsometry.

We establish the ultimate limits that quantum theory imposes on the accuracy attainable in optical ellipsometry. We show that the standard quantum limit, as usually reached when the incident light is in a coherent state, can be surpassed with the use of appropriate squeezed states and, for tailored beams, even pushed to the ultimate Heisenberg limit.

Universal Compressive Characterization of Quantum Dynamics.

Recent quantum technologies utilize complex multidimensional processes that govern the dynamics of quantum systems. We develop an adaptive diagonal-element-probing compression technique that feasibly characterizes any unknown quantum processes using much fewer measurements compared to conventional methods. This technique utilizes compressive projective measurements that are generalizable to an arbitrary number of subsystems.

Non-Euclidean symmetries of first-order optical systems.

We revisit the basic aspects of first-order optical systems from a geometrical viewpoint. In the paraxial regime, there is a wide family of beams for which the action of these systems can be represented as a Möbius transformation. We examine this action from the perspective of non-Euclidean hyperbolic geometry and resort to the isometric-circle method to decompose it as a reflection followed by an inversion in a circle.

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.

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.

Omnidirectional reflection from generalized Fibonacci quasicrystals.

We determine the optimal thicknesses for which omnidirectional reflection from generalized Fibonacci quasicrystals occurs. By capitalizing on the idea of wavelength- and angle-averaged reflectance, we assess in a consistent way the performance of the different systems. Our results indicate that some of these aperiodic arrangements can largely over-perform the conventional photonic crystals as omnidirectional reflection is concerned.

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.