Exploring the ultimate limits: super-resolution enhanced by partial coherence.

The resolution of separation of two elementary signals forming a partially coherent superposition, defined by quantum Fisher information and normalized with respect to detection probabilities, is always limited by the resolution of incoherent mixtures. However, when the partially coherent superpositions are prepared in a controlled way, the precision can be enhanced by up to several orders of magnitude above this limit. Coherence also allows the sorting of information about various parameters into distinct channels as demonstrated by the parameter of separation linked with the anti-phase superposition and the centroid position linked with the in-phase superposition.

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.

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.

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.

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.

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.

Quantification of entanglement by means of convergent iterations.

The relative entropy of entanglement of a given bipartite quantum state is calculated by means of a convergent iterative algorithm. When this state turns out to be nonseparable, the algorithm also provides the corresponding optimal entanglement-witness measurement.