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Stimulated parametric down-conversion is a nonlinear optical process in which the orbital angular momentum of light is conserved under most practical conditions. However, there are instances in which the topological charge is not compatible with the remaining modal structure of the stimulated idler beam. As a result, the stimulated down-converted light diffracts and gives rise to Laguerre-Gaussian-like beams with nonzero radial indices. We present a theoretical and experimental analysis demonstrating this fundamental aspect of nonlinear processes with light beams possessing orbital angular momentum.

We develop a method to characterize arbitrary superpositions of light orbital angular momentum (OAM) with high fidelity by using astigmatic transformation and machine-learning processing. In order to identify each superposition unequivocally, we combine two intensity measurements. The first one is the direct image of the input beam, which is invariant for positive and negative OAM components. The second one is an image obtained using an astigmatic transformation, which allows distinguishing between positive and negative topological charges. Samples of these image pairs are used to train a convolution neural network and achieve high-fidelity recognition of arbitrary OAM superpositions.

Preparation, control, and measurement of optical vortices are increasingly important, as they play essential roles in both fundamental science and optical technology applications. Spatial light modulation is the main approach behind the control strategies, although there are limitations concerning the controllable wavelength. It is therefore crucial to develop approaches that expand the spectral range of light modulation. Here, we demonstrate the modulation of light by light in nonlinear optical interactions to demonstrate the identification of the topological charge of optical vortices. A triangular-lattice pattern is observed in light beams resulting from the spatial cross modulation between an optical vortex and a triangular shaped beam undergoing parametric interaction. Both up- and downconversion processes are investigated, and the far-field image of the converted beam exhibits a triangular lattice. The number of sites and the lattice orientation are determined by the topological charge of the vortex beam. In the downconversion process, the lattice orientation can also be affected by phase conjugation. The observed cross modulation works for a large variety of spatial field structures. Our results show that modulation of light by light can be used at wavelengths for which solid-state devices are not yet available.

We report on an experiment that investigates the spatial mode conversion in the process of parametric down-conversion seeded by a light beam in a superposition of orbital angular momentum modes. This process is interpreted in terms of a geometric representation of first-order spatial modes in a Poincar\'e sphere, providing an intuitive image of the phase conjugation and the topological charge conservation. We also make a comparison with the analogous phenomenon for optical parametric oscillators., Comment: 5 pages, 6 figures

A vector vortex beam presents local polarization states that are spatially modulated in the plane transverse to propagation. By employing a two-crystal-sandwich source allowing for nonlinear interactions between input fields of any polarization, we analyze experimentally the process of stimulated parametric down-conversion and observe unique effects when the pump and seed fields are vector vortex beams. We reconstruct the transverse polarization pattern of the generated idler beam by Stokes polarimetry. The experimental results obtained are in good qualitative agreement with theory and exhibit manifold polarization transverse distributions for different combinations of pump and seed vector vortex beams, which may find applications in both classical and quantum optics.

We demonstrate that a triangular cavity can operate as an efficient discriminator for Hermite-Gaussian optical modes. The process is applied to distinct fields produced by a Spatial Light Modulator, decomposing the generated paraxial field onto a basis of modes defined by the resonant modes of the optical cavity. We also present a proposal for the realization of a mode sorter based on a sequence of these cavities, without the need for optical isolation. We discuus its possible applications in sensitive measurements and distribution of information in optical systems. The high purity of the process should enable the use at the level of quantum information sharing., Comment: 9 pages, 9 figures

We present a quantum optics approach for describing stimulated parametric down conversion in the two type-I crystal "sandwich" configuration, which allows for parametric interaction of vector vortex beams. We analyze the conditions for which phase conjugation of the seed vector beam occurs. We then use two strategies for defining generalized Stokes parameters to describe phase conjugation of vector vortex beams. These allow for geometrical representations, such as higher-order Poincar\'e spheres. Our results are useful for description and design of stimulated and spontaneous parametric down conversion experiments with vector vortex beams., Comment: 11 pages, 6 figures

The generalized amplitude damping (GAD) quantum channel implements the interaction between a qubit and an environment with arbitrary temperature and arbitrary interaction time. Here, we implement a photonic version of the GAD for the case of infinite interaction time (full thermalization). We also show that this quantum channel works as a thermal bath with controlled temperature., Comment: 5 pages, 3 figures

Optical modes possessing orbital angular momentum constitute a very useful platform for experimental studies on the quantum limits of Thermodynamics. Here, we present experimental results for entangled photon pairs subjected to thin turbulence simulated with spatial light modulators and interpret them in the context of the generalized Jarzysnki's fluctuation relation. By holographic measurement of the orbital angular momentum, we obtain the work distribution produced by the turbulence for single and double-sided turbulence channels. The use of the Klyshko's advanced wave picture allows us to interpret the experimental scheme as two-way processes in a fully quantum picture., Comment: 10 pages, 11 figures, two new appendices

The study of non-equilibrium physics from the perspective of the quantum limits of thermodynamics and fluctuation relations can be experimentally addressed with linear optical systems. We discuss recent experimental investigations in this scenario and present new proposed schemes while discussing the potential advances they could bring to the field of quantum thermodynamics.

The advanced-wave picture is "... an intuitive treatment of two-photon correlation with the help of the concept of an effective field acting upon one of the two detectors and formed by parametric conversion of the advanced wave emitted by the second detector ..." [A. V. Belinskii and D. N. Klyshko, JETP 78, 259 (1994)]. This quote from Belinskii and Klyshko nicely describes the concept of the advanced-wave picture; an intuitive tool for designing and predicting results from coincidence-based two-photon experiments. Up to now, the advanced-wave picture has been considered primarily for the case of an ideal plane-wave pump beam and only for design purposes. Here we study the advanced wave picture for a structured pump beam and in the context of stimulated emission provoked by an auxiliary input laser beam. This suggests stimulated parametric down-conversion as a useful experimental tool for testing the experimental sets designed with the advanced-wave picture. We present experimental results demonstrating the strategy of designing the experiment with advanced-wave picture and testing with stimulated emission., 11 pages, 10 figures

Continuous variables systems find valuable applications in quantum information processing. To deal with an infinite-dimensional Hilbert space, one in general has to handle large numbers of discretized measurements in tasks such as entanglement detection. Here we employ the continuous transverse spatial variables of photon pairs to experimentally demonstrate novel entanglement criteria based on a periodic structure of coarse-grained measurements. The periodization of the measurements allows for an efficient evaluation of entanglement using spatial masks acting as mode analyzers over the entire transverse field distribution of the photons and without the need to reconstruct the probability densities of the conjugate continuous variables. Our experimental results demonstrate the utility of the derived criteria with a success rate in entanglement detection of $\sim60\%$ relative to $7344$ studied cases., V1: revtex4, 10 pages, 4 figures + supp. material (4 pages, 1 figure) V2: Substantial revisions implemented both in theory and experimental data analysis

Non-equilibrium thermodynamics and quantum information theory are interrelated research fields witnessing an increasing interest, both theoretical and experimental. This is manly due to the broadness of these theories, which found applications in many different fields of science, ranging from biology to the foundations of physics. Here, by employing the orbital angular momentum of light, we propose a new platform for studying non-equilibrium properties of high dimensional quantum systems. Specifically, we use Laguerre-Gaussian beams to emulate the energy eigenstates of a two-dimension quantum harmonic oscillator having angular momentum. These light beams are subjected to a process realized by a spatial light modulator and the corresponding work distribution is experimentally reconstructed employing a two-point measurement scheme. The Jarzynski fluctuation relation is then verified. We also demonstrate the operation of the system as a Maxwell's demon.

We present a proposal of a set-up to measure the work distribution due to an arbitrary unitary process acting on the spatial transverse degrees of freedom of a light beam. Hermite-Gaussian optical modes representing a quantum harmonic oscillator are prepared in a thermal state and sent through an interferometer. We show that the Fourier transform of the work distribution, or the characteristic function, can be obtained by measuring the intensity at the output of the interferometer. The usefulness of the approach is illustrated by calculating the work distribution for a unitary operation that displaces the linear momentum of the oscillator. We discuss the feasibility of the experiment, which can be realized with simple linear optical components., Comment: 12 pages, 10 figures, accepted for publication in Physical Review A

Recently [Cavalcanti \textit{et al.} Nat Commun \textbf{6}, 7941 (2015)] proposed a method to certify the presence of entanglement in asymmetric networks, where some users do not have control over the measurements they are performing. Such asymmetry naturally emerges in realistic situtations, such as in cryptographic protocols over quantum networks. Here we implement such "semi-device independent" techniques to experimentally witness all types of entanglement on a three-qubit photonic W state. Furthermore we analise the amount of genuine randomness that can be certified in this scenario from any bipartition of the three-qubit W state., v2: text improved, steering witness redefined so that their violation provides the steering robustness, experimental data included in an appendix

We demonstrate the difference between local, single-particle dynamics and global dynamics of entangled quantum systems coupled to independent environments. Using an all-optical experimental setup, we showed that, even when the environment-induced decay of each system is asymptotic, quantum entanglement may suddenly disappear. This “sudden death” constitutes yet another distinct and counterintuitive trait of entanglement.

We discuss a simple experiment illustrating the fundamentals of quantum cryptography. Our experiment is performed using novel complementary observables: the transverse position and momentum of photons. In the classical optics regime the experiment serves as an interesting and simple classroom demonstration of the principles of quantum key distribution.

Orbital angular momentum exchange, both in cavity free stimulated parametric down conversion and in an optical parametric oscillator, is studied. In both cases, the conditions for parametric amplification are discussed in terms of the orbital angular momentum exchange between the interacting fields. It is shown that in cavity free parametric down conversion, parametric amplification is conditioned to conserve orbital angular momentum. However, for parametric oscillation, cavity and anisotropy effects play a crucial role in the orbital angular momentum exchange between the interacting fields.

Twin photons can be entangled in transverse momentum and position, giving rise to the so-called quantum images. The term quantum image has been used for images measured with photon coincidence schemes, also called correlated images. Some kinds of correlated images are prepared by transferring the angular spectrum of the pump beam to the correlated twin beams. In this case, it is possible to show that transverse correlations can violate a classical inequality, leading to spatial photon anti-bunching. We briefly review the use of the transfer of the angular spectrum in the production of these non-classical correlations. In addition, we demonstrate experimentally that the quantum image can be prepared partially through the nonlinear interaction and partially by propagation of signal and idler beams through lenses. Using this kind of preparation it is also possible to use a telescope for transmitting the quantum image, compensating the divergence of signal and idler beams.

We demonstrate theoretical and experimentally how it is possible to manipulate an entangled angular spectrum of twin beams, in order to reconstruct correlated images with coincidence detection. The entangled angular spectrum comes from the pump and the image is obtained only if signal and idler are properly treated., Comment: Submitted for publication in Optics Communications

We discuss how it is possible to manipulate quantum spatial properties of light beams by using the transfer of the angular spectrum. Twin beams from the parametric down-conversion can be prepared in a state that carries two different quantum images. At the same time, the twin photons can be entangled in polarization. This preparation allows the selection between the detection of each one of the images at a time or a mixture by performing proper projections onto polarization sub-spaces. As another example, we show how to produce a light beam presenting spatial anti-bunching through the control of the entangled angular spectrum and reflections.

Sources of entangled photon pairs using two parametric down-converters are capable of generating interchangeable entanglement in two different degrees of freedom. The connection between these two degrees of freedom allows the control of the entanglement properties of one, by acting on the other degree of freedom. We demonstrate experimentally, the quantum distillation of the position entanglement using polarization analyzers., Submitted for publication in Optics Communications

Using two parametric down-converters, it is possible to prepare twin photons in position-entangled states, where the photons are labelled by their birth position. We have measured the interference between the two probability amplitudes for a twin-photon pair: of being born in the first crystal or in the second one. The oscillation frequency of the coincidence pattern can be varied through independent phase differences in the signal and idler beams. Entangled states in position and also in the polarization sub-space can be prepared with this source. In this case, measurement of the position interference can give us information about the degree of polarization entanglement.

Exchange of information between a quantum system and its surrounding environment plays a fundamental role in the study of the dynamics of open quantum systems. Here we discuss the role of the information exchange in the non-Markovian behavior of dynamical quantum processes following the decoherence approach, where we consider a quantum system that is initially correlated with its measurement apparatus, which in turn interacts with the environment. We introduce a new way of looking at the information exchange between the system and environment using the quantum loss, which is shown to be closely related to the measure of non-Markovianity based on the quantum mutual information. We also extend the results of [Phys. Rev. Lett. 112, 210402 (2014)] by Fanchini et al. in several directions, providing a more detailed investigation of the use of the accessible information for quantifying the backflow of information from the environment to the system. Moreover, we reveal a clear conceptual relation between the entanglement and mutual information based measures of non-Markovianity in terms of the quantum loss and accessible information. We compare different ways of studying the information flow in two theoretical examples. We also present experimental results on the investigation of the quantum loss and accessible information for a two-level system undergoing a zero temperature amplitude damping process. We use an optical approach that allows full access to the state of the environment., 11 pages, 7 figures

When an initially entangled pair of qubits undergoes local decoherence processes, there are a number of ways in which the original entanglement can spread throughout the multipartite system consisting of the two qubits and their environments. Here we report theoretical and experimental results regarding the dynamics of the distribution of entanglement in this system. The experiment employs an all optical set-up in which the qubits are encoded in the polarization degrees of freedom of two photons, and each local decoherence channel is implemented with an interferometer that couples the polarization to the path of each photon, which acts as an environment. We monitor the dynamics and distribution of entanglement and observe the transition from bipartite to multipartite entanglement and back, and show how these transitions are intimately related to the sudden death and sudden birth of entanglement. The multipartite entanglement is further analyzed in terms of 3- and 4- partite entanglement contributions, and genuine four-qubit entanglement is observed at some points of the evolution., 6 pages, 4 figures

We demonstrate the use of a phase-only spatial light modulator for the measurement of transverse spatial distributions of coincidence counts between twin photon beams, in a fully automated fashion. This is accomplished by means of the polarization dependence of the modulator, which allows the conversion of a phase pattern into an amplitude pattern. We also present a correction procedure, that accounts for unwanted coincidence counts due to polarization decoherence effects.

Spatial light modulators are versatile devices employed in a vast range of applications to modify the transverse phase or amplitude profile of an incident light beam. Most experiments are designed to use a specific polarization which renders optimal sensitivity for phase or amplitude modulation. Here we take a different approach and apply the formalism of quantum information to characterize how a phase modulator affects a general polarization state. In this context, the spatial modulators can be exploited as a resource to couple the polarization and the transverse spatial degrees of freedom. Using a quasi-monochromatic single photon beam obtained from a pair of twin photons generated by spontaneous parametric down conversion, we performed quantum process tomography in order to obtain a general analytic model for a quantum channel that describes the action of the device on the polarization qubits. We illustrate the application of these concepts by demonstrating the implementation of a controllable phase flip channel. This scheme can be applied in a straightforward manner to characterize the resulting polarization states of different types of phase or amplitude modulators and motivates the combined use of polarization and spatial degrees of freedom in innovative applications., 7 pages, 7 figures

A measurement-based quantum computer could consist of a local-gapped Hamiltonian system, whose thermal states --at sufficiently low temperature-- are universal resources for the computation. Initialization of the computer would correspond to cooling the system. We perform an experimental quantum simulation of such cooling process with entangled photons. We prepare three-qubit thermal cluster states exploiting the equivalence between local dephasing and thermalisation for these states. This allows us to tune the system's temperature by changing the dephasing strength. We monitor the entanglement as the system cools down and observe the transitions from separability to bound entanglement, and then to free entanglement. We also analyze the performance of the system for measurement-based single-qubit state preparation. These studies constitute a basic characterisation of experimental cluster-state computation under imperfect conditions., 5 pages, 4 figures

The open-system dynamics of entanglement plays an important role in the assessment of the robustness of quantum information processes and also in the investigation of the classical limit of quantum mechanics. Here we show that, subjacent to this dynamics, there is a subtle flow of quantum correlations. We use a recently proposed optical setup, which allows joint tomography of system and environment, to show that the decay of an initial bipartite entangled state leads to the build up of multipartite entanglement and quantum discord, the latter exhibiting a non-analytic behavior that signals the emergence of maximal genuine quantum entanglement. The origin of this analyticity is shown to be distinct from similar behavior previously found in bipartite systems. Monogamy relations within the context of open-system dynamics explain this new phenomenon., 12 pages, 13 figures, comments welcome

The degree of non-Markovianity of quantum processes has been characterized in several different ways in the recent literature. However, the relationship between the non-Markovian behavior and the flow of information between the system and the environment through an entropic measure has not been yet established. We propose an entanglement-based measure of non-Markovianity by employing the concept of assisted knowledge, where the environment E, acquires information about a system S, by means of its measurement apparatus A. The assisted knowledge, based on the accessible information in terms of von-Neumann entropy, monotonically increases in time for all Markovian quantum processes. We demonstrate that the signatures of non-Markovianity can be captured by the nonmonotonic behaviour of the assisted knowledge. We explore this scenario for a two-level system undergoing a relaxation process, through an experimental implementation using an optical approach that allows full access to the state of the environment., Final Version

Multipartite entanglement is very poorly understood despite all the theoretical and experimental advances of the last decades. Preparation, manipulation and identification of this resource is crucial for both practical and fundamental reasons. However, the difficulty in the practical manipulation and the complexity of the data generated by measurements on these systems increase rapidly with the number of parties. Therefore, we would like to experimentally address the problem of how much information about multipartite entanglement we can access with incomplete measurements. In particular, it was shown that some types of pure multipartite entangled states can be witnessed without measuring the correlations [M. Walter et al., Science 340, 1205 (2013)] between parties, which is strongly demanding experimentally. We explore this method using an optical setup that permits the preparation and the complete tomographic reconstruction of many inequivalent classes of three- and four-partite entangled states, and compare complete versus incomplete information. We show that the method is useful in practice, even for non-pure states or non ideal measurement conditions., Comment: 12 pages, 7 figures. Close to published version

We experimentally implement an optical algorithm for integration of a real-valued bivariate func- tion. A user-defined function is encoded in the position-dependent phase of one of the polarization components of an optical beam. The integral of this function is retrieved by measuring a Stokes parameter of the polarization. We analyze the performance of the system as an integration device.

We report on an experiment showing that the wavelength of a biphoton is clearly dependent onthe measurement scheme and on the way it is defined. It is shown that it can take any value, depending on the control of the interferometer phase differences. It is possible to identify the interference of the single and two-photon wavepackets as particular cases of the most general interference process. The variable wavelength has no implication on the energy of the individual photons neither on the total energy of the biphoton.

We show that the first experiment with double-slits and twin photons detected in coincidence can be understood as a quantum eraser. The ``which path'' information is erased by transverse indistinguishability obtained by means of mode filtering in the twin conjugated beam. A delayed choice quantum eraser based on the same scheme is proposed., Comment: Submitted for publication in Optics Communications

We report an interference experiment in which photon pairs generated by spontaneous parametric down-conversion produce a Young-type fourth-order interference pattern after being scattered by two different and spatially separated apertures, whose superposition defines a double slit. The experiment is compared with previous ones based on parametric down-conversion, and its nonlocal nature is discussed. A theoretical explanation is also provided.

We show that the two-photon state generated in the process of spontaneous parametric down-conversion in a thin crystal carries information about the angular spectrum of the pump beam. This information transfer allows one to control the transverse correlation properties of the down-converted fields by manipulating the pump field, with consequences for a broad class of experiments. The effect is demonstrated theoretically and experimentally, in connection with the formation of fourth-order images by the down-converted beams.

Nearly all protocols requiring shared quantum information--such as quantum teleportation or key distribution--rely on entanglement between distant parties. However, entanglement is difficult to characterize experimentally. All existing techniques for doing so, including entanglement witnesses or Bell inequalities, disclose the entanglement of some quantum states but fail for other states; therefore, they cannot provide satisfactory results in general. Such methods are fundamentally different from entanglement measures that, by definition, quantify the amount of entanglement in any state. However, these measures suffer from the severe disadvantage that they typically are not directly accessible in laboratory experiments. Here we report a linear optics experiment in which we directly observe a pure-state entanglement measure, namely concurrence. Our measurement set-up includes two copies of a quantum state: these 'twin' states are prepared in the polarization and momentum degrees of freedom of two photons, and concurrence is measured with a single, local measurement on just one of the photons.

Among interference effects that have been observed using parametric down-conversion light, some experiments show that second and fourth order interference effects can be observed between independent light beams. Also, it has been shown that the presence of mirrors reflecting the pump and the down converted beams can give rise to interference effects. In this paper we show that these mirror effects can be explained alternatively by means of a coherence induced between initially independent beams. Our analysis is based on a longitudinal multimode approach and leads to intensity and coincidence distributions and fringe visibilities. We also present experimental results showing that mirror effects can be observed even using a pump beam with a coherence length much smaller than the distance between crystal and pump mirror.

We report an experiment in which the moments of spatial coordinates of down-converted photons are measured directly, without having to reconstruct any marginal probability distributions. We use a spatial light modulator to couple the spatial degrees of freedom and the polarization of the fields, which act as ancilla systems. Information about the spatial correlations is obtained via measurements on the ancilla qubits. Among other applications, this new method provides a more efficient technique to identify continuous variable entanglement., Comment: 6 pages (4+Supplementary Information), 3 figures

The transverse spatial properties of the twin light beams of the down-conversion have been recently investigated in experiments using double-slit and coincidence measurements. Fringes are obtained, with a controlled degree of visibility, placing the slits in the signal beam and scanning the signal detector [direct interference---Phys. Rev. A 49, 4176 (1994)] and also, for the degenerated type II down-conversion, with slits in the signal beam and scanning the idler detector [ghost interference---Phys. Rev. Lett. 74, 3600 (1995)]. The idea of a ghost source is used to discuss the direct interference experiment. Using a nondegenerated type I down-conversion, experimental results are obtained showing that the visibility of the ghost interference patterns can be controlled by the ghost source size, analogously as it can be done for a real light source. \textcopyright{} 1996 The American Physical Society.

We use the classical correlation between a quantum system being measured and its measurement apparatus to analyze the amount of information being retrieved in a quantum measurement process. Accounting for decoherence of the apparatus, we show that these correlations may have a sudden transition from a decay regime to a constant level. This transition characterizes a non-asymptotic emergence of the pointer basis, while the system-apparatus can still be quantum correlated. We provide a formalization of the concept of emergence of a pointer basis in an apparatus subject to decoherence. This contrast of the pointer basis emergence to the quantum to classical transition is demonstrated in an experiment with polarization entangled photon pairs., Comment: 4+2 pgs, 3 figures. Title changed. Revised version to appear on PRL

The perception that quantum correlations can still appear in separable states has opened exciting new possibilities regarding their use as a resource in quantum information science. Quantifying such quantum correlations involves the complete knowledge of the system's state and numerical optimization procedures. Thus, it is natural to seek methods involving fewer measurements that indicate the nature of the correlations in a system. Here we propose a classicality witness that can be accurately estimated via statistics from a single measurement and perform an experiment to explore the utility of this witness for quantum states with different types of correlations.

We discuss the use of the transverse spatial degrees of freedom of photons propagating in the paraxial approximation for continuous variable information processing. Given the wide variety of linear optical devices available, a diverse range of operations can be performed on the spatial degrees of freedom of single photons. Here we show how to implement a set of continuous quantum logic gates which allow for universal quantum computation. In contrast with the usual quadratures of the electromagnetic field, the entire set of single photon gates for spatial degrees of freedom does not require optical nonlinearity and, in principle, can be performed with a single device: the spatial light modulator. Nevertheless, nonlinear optical processes, such as four-wave mixing, are needed in the implementation of two-photon gates. The efficiency of these gates is at present very low, however small scale investigations of continuous variable quantum computation are within the reach of current technology. In this regard, we show how novel cluster states for one-way quantum computing can be produced using spontaneous parametric down conversion., 11 pages, 6 figures

The nonconservation of entanglement, when two or more particles interact, sets it apart from other dynamical quantities, like energy and momentum, and does not allow the interpretation of the subtle dynamics of entanglement as a flow of this quantity between the constituents of the system. Nevertheless, we show that when the interaction between a qubit and its environment is described by an amplitude-decay channel, the conservation of the mean excitation number and the inclusion of a third party leads to an invariant expression involving the bipartite entanglement between each of the parties and the other two. We provide an experimental demonstration of this idea using entangled photons and generalize it to $N$-partite Greenberger-Horne-Zeilinger states.