Structured light refers to the generation and application of custom light fields. As the tools and technology to create and detect structured light have evolved, steadily the applications have begun to emerge. This roadmap touches on the key fields within structured light from the perspective of experts in those areas, providing insight into the current state and the challenges their respective fields face. Collectively the roadmap outlines the venerable nature of structured light research and the exciting prospects for the future that are yet to be realized.

Entanglement of the properties of two separated particles constitutes a fundamental signature of quantum mechanics and is a key resource for quantum information science. We demonstrate strong Einstein, Podolsky, and Rosen correlations between the angular position and orbital angular momentum of two photons created by the nonlinear optical process of spontaneous parametric down-conversion. The discrete nature of orbital angular momentum and the continuous but periodic nature of angular position give rise to a special sort of entanglement between these two variables. The resulting correlations are found to be an order of magnitude stronger than those allowed by the uncertainty principle for independent (nonentangled) particles. Our results suggest that angular position and orbital angular momentum may find important applications in quantum information science.

Quantum mechanics allows events to happen with no definite causal order: this can be verified by measuring a causal witness, in the same way that an entanglement witness verifies entanglement. Here, we realize a photonic quantum switch, where two operations andB act in a quantum superposition of their two possible orders. The operations are on the transverse spatial mode of the photons; polarization coherently controls their order. Our implementation ensures that the operations cannot be distinguished by spatial or temporal position-further it allows qudit encoding in the target. We confirm our quantum switch has no definite causal order by constructing a causal witness and measuring its value to be 18 standard deviations beyond the definite-order bound. DOI: 10.1103/PhysRevLett.121.090503 In daily experience, it is natural to think of events happening in a fixed causal order. Strikingly, it has been proposed that quantum physics allows for nonclassical causal structures where the order of events is indefinite [1,2]. It has been theoretically shown that such a possibility provides an advantage for computation [3], communication complexity [4,5], and other information processing tasks [6][7][8]. Furthermore, investigations of indefinite causal orders suggest a promising route towards a theory that combines general relativity and quantum mechanics [9,10].Indefinite causal orders can be studied using a framework that distinguishes whether some experimental situationcalled a "process"-is compatible with a fixed causal order of the events or not. An example of a process with indefinite causal order is the "quantum switch" [1]. In the quantum switch, the order in which two quantum operation andBconsidered as "black box operations"-are performed on a target system is coherently controlled by a control quantum system (Fig. 1). This can also be seen as a particular case of "superposition of time evolution" [11]. The advantages provided by the quantum switch arise from the fact that it cannot be reproduced by an ordinary quantum circuit which uses the same number of black box operations [3][4][5][6][7].Here, we present an optical implementation of the quantum switch where the control system is the photon's polarization and the target is the transverse spatial mode. We verify indefinite causal order by introducing a causal witness [14,15], for which we obtain a value 18 standard deviations beyond the bound for definite ordering. One notable achievement of our experiment is that it opens the possibility of encoding more than two levels in the target system-transverse spatial mode can indeed be highdimensional and hence can act as a qudit.In previous implementations [12,13], the location of each black box-the spot where photons go through a set of wave plates-was different depending on the order, resulting in four distinct locations in space [ Fig. 1(c)]. Furthermore, the photons had a coherence length much shorter than the distance between the two sets of wave plates: in effect, the operations could also be distinct in...

Abstract:That the speed of light in free space is constant is a cornerstone of modern physics. However, light beams have finite transverse size, which leads to a modification of their wavevectors resulting in a change to their phase and group velocities. We study the group velocity of single photons by measuring a change in their arrival time that results from changing the beam's transverse spatial structure. Using time-correlated photon pairs we show a reduction of the group velocity of photons in both a Bessel beam and photons in a focused Gaussian beam. In both cases, the delay is several micrometers over a propagation distance of the order of 1 m. Our work highlights that, even in free space, the invariance of the speed of light only applies to plane waves. Main textThe speed of light is trivially given as / , where is the speed of light in free space and is the refractive index of the medium. In free space, where = 1, the speed of light is simply . We show that the introduction of transverse structure to the light beam reduces the group velocity by an amount depending upon the aperture of the optical system. The delay corresponding to this reduction in the group velocity can be greater than the optical wavelength and consequently should not be confused with the HÀ Gouy phase shift (1, 2). To emphasize that this effect is both a linear and intrinsic property of light, we measure the delay as a function of the transverse spatial structure of single photons.The slowing down of light that we observe in free space should also not be confused with slow, or indeed fast, light associated with propagation in highly nonlinear or structured materials (3,4). Even in the absence of a medium, the modification of the speed of light has previously been known. For example, within a hollow waveguide, the wavevector along the guide is reduced below the free-space value, leading to a phase velocity greater than . Within the hollow waveguide, the product of the phase and group velocities is given as , = 2 , thereby resulting in a group velocity , along the waveguide less than (5). 2Although this relation for group and phase velocities is derived for the case of a hollow waveguide, the waveguide material properties are irrelevant. It is the transverse spatial confinement of the field that leads to a modification of the axial component of the wavevector, . In general, for light of wavelength , the magnitude of the wavevector, 0 = 2 / , and its Cartesian components { , , } are related through (5)All optical modes of finite , spatial extent require non-zero and , which implies < 0 , giving a corresponding modification of both the phase and group velocities of the light. In this sense, light beams with non-zero k x and k y are naturally dispersive, even in free space. Extending upon the case of a mode within a hollow waveguide, an example of a structured beam is a Bessel beam (Fig. 1A), which is itself the description of a mode within a circular waveguide (1, 6). In free space, Bessel beams can be created using an axicon, or its dif...

We observe entanglement between photons in controlled super-position states of orbital angular momentum (OAM). By drawing a direct analogy between OAM and polarization states of light, we demonstrate the entangled nature of high order OAM states generated by spontaneous downconversion through violation of a suitable Clauser Horne Shimony Holt (CHSH)-Bell inequality. We demonstrate this violation in a number of two-dimensional subspaces of the higher dimensional OAM Hilbert space.

Integrated photonics will play a key role in quantum systems as they grow from few-qubit prototypes to tens of thousands of qubits. The underlying optical quantum technologies can only be realized through the integration of these components onto quantum photonic integrated circuits (QPICs) with accompanying electronics. In the last decade, remarkable advances in quantum photonic integration have enabled table-top experiments to be scaled down to prototype chips with improvements in efficiency, robustness, and key performance metrics. These advances have enabled integrated quantum photonic technologies combining up to 650 optical and electrical components onto a single chip that are capable of programmable quantum information processing, chip-to-chip networking, hybrid quantum system integration, and high-speed communications. In this roadmap article, we highlight the status, current and future challenges, and emerging technologies in several key research areas in integrated quantum photonics, including photonic platforms, quantum and classical light sources, quantum frequency conversion, integrated detectors, and applications in computing, communications, and sensing. With advances in materials, photonic design architectures, fabrication and integration processes, packaging, and testing and benchmarking, in the next decade we can expect a transition from single- and few-function prototypes to large-scale integration of multi-functional and reconfigurable devices that will have a transformative impact on quantum information science and engineering.

We demonstrate the contrast enhancement of images within a ghost-imaging system by use of nonlocal phase filters. We use parametric down-conversion as the two-photon light source and two separated phase modulators, in the signal and idler arms which represent different phase filters and objects, respectively. We obtain edge enhanced images as a direct consequence of the quantum correlations in the orbital angular momentum (OAM) of the down-converted photon pairs. For phase objects, with differently orientated edges, we show a violation of a Bell-type inequality for an OAM subspace, thereby unambiguously revealing the quantum nature of our ghost-imaging arrangement.

Any practical experiment utilising the innate D-dimensional entanglement of the orbital angular momentum (OAM) state space of photons is subject to the modal capacity of the detection system. We show that given such a constraint, the number of measured, entangled OAM modes in photon pairs generated by spontaneous parametric down-conversion (SPDC) can be maximised by tuning the phase-matching conditions in the SPDC process. We demonstrate a factor of 2 increase on the half-width of the OAM-correlation spectrum, from 10 to 20, the latter implying ≈ 50 -dimensional two-photon OAM entanglement. Exploiting correlations in the conjugate variable, angular position, we measure concurrence values 0.96 and 0.90 for two phase-matching conditions, indicating bipartite, D-dimensional entanglement where D is tuneable.PACS numbers: 03.65. Ud, 03.67.Bg, 03.67.Mn Much attention has been directed to the twodimensional state space of photon polarisation which provides both a conceptually and experimentally accessible playground [1][2][3]. D-dimensional two-photon entanglement, wherein each photon is a D-level quDit taking on any of D possible values, is an even more fertile playground. From a fundamental standpoint, higherdimensional entanglement implies stronger violations of locality [4,5] and is especially useful in the study of mutually unbiased bases in higher dimensions [6]. More relevant to practical applications, higher-dimensional entanglement provides higher information capacity [7,8] and increased security and robustness [8,9]. Experimentally, D-levels in photons can be achieved by using the temporal and spectral degrees of freedom [10], polarisation of more than one photon [11], transverse spatial profile [7], position and linear momentum [12], and angular position and orbital angular momentum [13].The entanglement of orbital angular momentum (OAM) in photons generated via spontaneous parametric down-conversion (SPDC) is firmly established theoretically and experimentally [14,15]. The interest in OAM stems from its discrete and theoretically infinitedimensional Hilbert space. Since the pioneering experiment of Zeilinger and co-workers ten years ago, OAM and it conjugate variable, angular position, has been steadily gaining ground as a mainstream variable in which to observe quantum correlations. Bell-type and Leggett inequalities have both been violated in twodimensional OAM subspaces analogous to the experiments done previously for polarisation [16,17]. The innate high-dimensional nature of OAM entanglement has been verified in an Einstein-Podolsky-Rosen (EPR) type experiment which measured both OAM and angular position [13]. A Bell-type inequality for higher dimensions has been recently violated using OAM states demonstrating experimental, two-photon, 11-dimensional entanglement [5]. The number of entangled OAM states that can be measured, i.e. the measurement spiral bandwidth depends on both the detection capability and the number of OAM states that is generated by the down-conversion process, i.e. the generation...