Modal decomposition of light has been known for a long time, applied mostly to pattern recognition. With the commercialization of liquid-crystal devices, digital holography as an enabling tool has become accessible to all, and with it all-digital tools for the decomposition of light have finally come of age. We review recent advances in unravelling the properties of light, from the modal structure of laser beams to decoding the information stored in orbital angular momentum (OAM)-carrying fields. We show application of these tools to fiber lasers, solid-state lasers, and structured light created in the laboratory by holographic laser beam shaping. We show by experimental implementation how digital holograms may be used to infer the intensity, phase, wavefront, Poynting vector, polarization, and OAM density of some unknown optical field. In particular, we outline how virtually all the previous ISO-standard beam diagnostic techniques may be readily replaced with all-digital equivalents, thus paving the way for unravelling of light in real time. Such tools are highly relevant to the in situ analysis of laser systems, to mode division multiplexing as an emerging tool in optical communication, and for quantum information processing with entangled photons.

Creation and detection of optical modes with spatial light modulators

From the physical point of view entanglement witnesses define a universal tool for analysis and classification of quantum entangled states. From the mathematical point of view they provide highly nontrivial generalization of positive operators and they find elegant correspondence with the theory of positive maps in matrix algebras. We concentrate on theoretical analysis of various important notions like (in)decomposability, atomicity, optimality, extremality and exposedness. Several methods of construction are provided as well. Our discussion is illustrated by many examples enabling the reader to see the intricate structure of these objects. It is shown that the theory of entanglement witnesses finds elegant geometric formulation in terms of convex cones and related geometric structures.

Entanglement witnesses: construction, analysis and classification

From the physical point of view entanglement witnesses (EWs) define a universal tool for analysis and classification of quantum entangled states. From the mathematical perspective bipartite EWs provide highly non-trivial generalization of positive operators and establish elegant correspondence with the theory of positive maps in matrix algebras. We concentrate on theoretical analysis of various important notions like decomposability, atomicity, optimality, extremality and exposedness. Several methods of construction are provided as well. Our discussion is illustrated by many examples enabling the reader to see the intricate structure of these objects. It is shown that the theory of EWs finds elegant geometric formulation in terms of convex cones and related geometric structures.

https://iopscience.iop.org/article/10.1088/1751-8113/47/48/483001/pdf

Photons entangled in high dimensions are more resilient to noise, making them ideal for quantum communication applications.

https://link.aps.org/pdf/10.1103/PhysRevX.9.041042

Overcoming Noise in Entanglement Distribution

Correlated photon imaging, popularly known as ghost imaging, is a technique whereby an image is formed from light that has never interacted with the object. In ghost imaging experiments, two correlated light fields are produced. One of these fields illuminates the object, and the other field is measured by a spatially resolving detector. In the quantum regime, these correlated light fields are produced by entangled photons created by spontaneous parametric down-conversion. To date, all correlated photon ghost imaging experiments have scanned a single-pixel detector through the field of view to obtain spatial information. However, scanning leads to poor sampling efficiency, which scales inversely with the number of pixels, N, in the image. In this work, we overcome this limitation by using a time-gated camera to record the single- photon events across the full scene. We obtain high-contrast images, 90%, in either the image plane or the far field of the photon pair source, taking advantage of the Einstein-Podolsky-Rosen-like correlations in position and momentum of the photon pairs. Our images contain a large number of modes, >500, creating opportunities in low-light-level imaging and in quantum information processing.

https://iopscience.iop.org/article/10.1088/1367-2630/15/7/073032/pdf

EPR-based ghost imaging using a single-photon-sensitive camera

We investigate correlations among complementary observables. In particular, we show how to take advantage of mutually unbiased bases for the efficient detection of entanglement in arbitrarily high-dimensional, multipartite, and continuous-variable quantum systems. The introduced entanglement criteria are relatively easy to implement experimentally since they require only a few local measurement settings. In addition, we establish a link between the separability problem and the maximum number of mutually unbiased bases---opening an additional avenue in this long-standing open problem.

Theodor Adaktylos

Papers

Entanglement detection via mutually unbiased bases