Few years ago the possibility of coupling and inter-converting the spin and orbital angular momentum (SAM and OAM) of paraxial light beams in inhomogeneous anisotropic media was demonstrated. An important case is provided by wave-plates having a singular transverse pattern of the birefringent optical axis, with a topological singularity of charge q at the plate center, hence named "q-plates". The introduction of q-plates has given rise in a few years to a number of new results and to a significant progress in the field of orbital angular momentum of light. Particularly promising are the quantum photonic applications, because the polarization control of OAM allows the transfer of quantum information from the SAM qubit space to an OAM subspace of a photon and vice versa. In this paper, we review the development of the q-plate idea and some of the most significant results that have originated from it, and we will briefly touch on many other related findings concerning the interaction of the SAM and OAM of light.

Photons have been a flagship system for studying quantum mechanics, advancing quantum information science, and developing quantum technologies. Quantum entanglement, teleportation, quantum key distribution and early quantum computing demonstrations were pioneered in this technology because photons represent a naturally mobile and low-noise system with quantum-limited detection readily available. The quantum states of individual photons can be manipulated with very high precision using interferometry, an experimental staple that has been under continuous development since the 19th century. The complexity of photonic quantum computing device and protocol realizations has raced ahead as both underlying technologies and theoretical schemes have continued to develop. Today, photonic quantum computing represents an exciting path to medium-and large-scale processing. It promises to out aside its reputation for requiring excessive resource overheads due to inefficient two-qubit gates. Instead, the ability to generate large numbers of photons-and the development of integrated platforms, improved sources and detectors, novel noise-tolerant theoretical approaches, and more-have solidified it as a leading contender for both quantum information processing and quantum networking. Our concise review provides a flyover of some key aspects of the field, with a focus on experiment. Apart from being a short and accessible introduction, its many references to in-depth articles and longer specialist reviews serve as a launching point for deeper study of the field. CONTENTS arXiv:1907.06331v1 [quant-ph]

"Twisted photons" are photons carrying a well-defined nonzero value of orbital angular momentum (OAM). The associated optical wave exhibits a helical shape of the wavefront (hence the name) and an optical vortex at the beam axis. The OAM of light is attracting a growing interest for its potential in photonic applications ranging from particle manipulation, microscopy, and nanotechnologies to fundamental tests of quantum mechanics, classical data multiplexing, and quantum communication. Hitherto, however, all results obtained with optical OAM were limited to laboratory scale. Here, we report the experimental demonstration of a link for free-space quantum communication with OAM operating over a distance of 210 m. Our method exploits OAM in combination with optical polarization to encode the information in rotation-invariant photonic states, so as to guarantee full independence of the communication from the local reference frames of the transmitting and receiving units. In particular, we implement quantum key distribution, a protocol exploiting the features of quantum mechanics to guarantee unconditional security in cryptographic communication, demonstrating error-rate performances that are fully compatible with real-world application requirements. Our results extend previous achievements of OAM-based quantum communication by over 2 orders of magnitude in the link scale, providing an important step forward in achieving the vision of a worldwide quantum network.

Quantum metrology exploits quantum correlations to perform measurements with precision higher than can be achieved with classical approaches. Photonic approaches promise transformative advances in the family of interferometric phase measurement techniques, a vital toolset used to precisely determine quantities including distance, velocity, acceleration and various materials properties [1][2][3].Without quantum enhancement, the precision limit in determining an unknown optical phase ϕ-i.e. the minimum uncertainty ∆ϕ-is the shot noise limit (SNL): ∆ϕ SN L = 1/ √ n, where n is the number of resources (e.g. photons) used. Entangled photons promise measurement sensitivity surpassing the shot noise limit achievable with classical probes. The maximally phase-sensitive state is a path-entangled state of definite number of photons N . Despite theoretical proposals stretching back decades [3,4], no measurement using such photonic (definite photon number) states has unconditionally surpassed the shot noise limit: by contrast, all demonstrations have employed postselection to discount photon loss in the source, interferometer or detectors. Here, we use an ultra-high efficiency source and high efficiency superconducting photon detectors to respectively make and measure a two-photon instance of the maximally-phase-sensitive NOON state, and use it to perform unconditional phase sensing beyond the shot noise limit-that is, without artificially correcting for loss or any other source of imperfection. Our results enable quantum-enahanced phase measurements at low photon flux and open the door to the next generation of optical quantum metrology advances.It has been known for several decades that probing with various optical quantum states can achieve phase super-sensitivity, i.e measurement of the phase with an uncertainty below the SNL [3,4]. It has been shown theoretically that multi-photon entangled states, such as NOON states, may achieve super-sensitivity and can, in principle, saturate the Heisenberg limit (HL), the ultimate bound on sensitivity [3,4,7]. For this reason, they are of great interest for maximising the information that can be collected per photon, which is useful for investigating sensitive samples [8]. NOON states are superpositions of N photons across two arms of an interferometer, each of which is a single optical mode:We use the term photonic to refer to states like this, because they possess definite photon number, and these photons are counted in detection. By contrast, we exclude from term "photonic" schemes using states of indefinite photon number and continuous wave-like measurement, such as squeezed states and homodyne detection. Such techniques have genuinely beaten the SNL, e.g. refs [5,6], but work over narrow bandwidths and cannot directly achieve the theoretical maximal sensitivity per resource. Super-resolution, however, is not enough by itself to surpass the SNL [9,20]: a high interference fringe visibility, and high transmission and detection efficiency are also required-they must exceed the t...