Scattering phenomena affect light propagation through any kind of medium from free space to biological tissues. Finding appropriate strategies to increase the robustness to scattering is the common requirement in developing both communication protocols and imaging systems. Recently, structured light has attracted attention due to its seeming scattering resistance in terms of transmissivity and spatial behavior. Moreover, correlation between optical polarization and orbital angular momentum (OAM), which characterizes the so-called vector vortex beam (VVB) states, seems to allow for the preservation of the polarization pattern. We extend the analysis by investigating both the spatial features and the polarization structure of vectorial optical vortexes propagating in scattering media with different concentrations. Among the observed features, we find a sudden swift decrease in contrast ratio for Gaussian, OAM, and VVB modes for concentrations of the adopted scattering media exceeding 0.09%. Our analysis provides a more general and complete study on the propagation of structured light in dispersive and scattering media.
Entanglement distribution between distant parties is one of the most important and challenging tasks in quantum communication. Distribution of photonic entangled states using optical fiber links is a fundamental building block toward quantum networks. Among the different degrees of freedom, orbital angular momentum (OAM) is one of the most promising due to its natural capability to encode high dimensional quantum states. We experimentally demonstrate fiber distribution of hybrid polarization-vector vortex entangled photon pairs. To this end, we exploit a recently developed air-core fiber that supports OAM modes. High fidelity distribution of the entangled states is demonstrated by performing quantum state tomography in the polarization-OAM Hilbert space after fiber propagation and by violations of Bell inequalities and multipartite entanglement tests. The results open new scenarios for quantum applications where correlated complex states can be transmitted by exploiting the vectorial nature of light.
Boson sampling is a computational problem that has recently been proposed as a candidate to obtain an unequivocal quantum computational advantage. The problem consists in sampling from the output distribution of indistinguishable bosons in a linear interferometer. There is strong evidence that such an experiment is hard to classically simulate, but it is naturally solved by dedicated photonic quantum hardware, comprising single photons, linear evolution, and photodetection. This prospect has stimulated much effort resulting in the experimental implementation of progressively larger devices. We review recent advances in photonic boson sampling, describing both the technological improvements achieved and the future challenges. We also discuss recent proposals and implementations of variants of the original problem, theoretical issues occurring when imperfections are considered, and advances in the development of suitable techniques for validation of boson sampling experiments. We conclude by discussing the future application of photonic boson sampling devices beyond the original theoretical scope.
The preparation of high-dimensional quan- tum states is of great significance in quantum information sci- ence and technology. Compared to qubits, qudit states – de- scribing quantum systems in d-dimensional spaces – enable stronger foundational tests of quantum mechanics [1–3] and better-performing applications in secure quantum communi- cations [4–9], quantum emulation [10, 11], quantum error cor- rection [12–14], fault-tolerant quantum computation [15–19], and quantum machine learning [20–22].
Needless to say, protocols performed on systems living in Hilbert spaces of large dimension require an increasing degree of control, in light of the large number of parameters required to describe states and operations. Nonetheless, the endeav- our of preparing arbitrary qudit states has been successfully achieved in various physical platforms [11, 23–32]. However, most of these works rely on ad hoc strategies, whose specific dependence on the underpinning dynamics makes their trans- lation across different physical platforms very difficult.
A very promising way to achieve the desired full inde- pendence of the physical platform, and thus a higher degree of universality, is the use of the rich dynamics offered by Quantum Walks (QWs) [33–35]. QWs, which can be thought of as the quantum counterparts of classical random walks, describe in their discrete version a high-dimensional qudit, named walker, embedded with an internal two-dimensional degree of freedom, conventionally dubbed coin. At every time step, the walker’s state moves coherently to the neighbouring sites in the lattice, conditionally to its coin state . QWs have been successfully implemented  in systems as di- verse as trapped atoms  and ions [39, 40], photonic cir- cuits [41–50], and optical lattices . Hence, an approach for state engineering based on their dynamics offers hope of being applicable effectively in a variety of different systems, independently of the details of the physical implementation.
While the QW dynamics was previously shown to allow the
engineering of specific walker’s states [52, 53], in Ref.  a scheme was proposed to use discrete-time QWs on a line to prepare arbitrary qudit states. This is achieved by enhanc- ing the degree of control over the walk’s dynamics through the arrangement of suitable step-dependent coin operations, which affect the coin-walker quantum correlations by de facto steering the state of the walker towards the desired final state, and finally projecting in the coin space. This last operation removes the correlations between walker and coin, thus pro- ducing a pure walker state with the desired features. In light of the large parameter space that characterizes the problem at hand, a systematic approach to the identification of the right set of coin operations and final projection is necessary. Such an analysis was presented in Ref. , in which a set of an- alytic conditions, together with suitable numerical optimiza- tions, was shown to guarantee the reaching of arbitrary target states with high probability.
In this paper, we make use of the scheme of Ref.  to give the first demonstration of a state-engineering protocol based on the controlled dynamics generated by QWs. We use the orbital angular momentum (OAM) degree of freedom of single-photon states as a convenient embodiment of the walker [48, 55, 56]. OAM-based experiments offer the pos- sibility to cover Hilbert spaces of large dimensions in light of the favourable (linear) scaling of the number of optical ele- ments with the size of the walk. Moreover, the scheme al- lows for the full control of the coin operation that is key to the implementation of the walk. In order to demonstrate the ver- satility of our scheme, we focus on the interesting classes of cat-like states and spin-coherent states [57, 58]. Those classes play a critical role in the exploration of the boundaries be- tween quantum and classical physics and whose implementa- tion is, in general, still a challenging task. Furthermore, we show experimentally the capability of engineering arbitrary states. The quality of the states synthesized in our endeavours, and the relative simplicity of the experimental protocol that we have put in place, demonstrate the effectiveness of a hybrid platform for quantum state engineering. Such platform holds together a programmable quantum system, the photonic QW in the angular momentum, and classical optimization al- gorithms for finding the best evolution to reach a certain quantum target.
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The progressive development of quantum technologies in many areas, ranging from investigation on foundamentals of quantum of mechanics to quantum information and computation, has increased the interest on those problems that can exhibit a quantum advantage. The Boson Sampling problem is a clear example where traditional computers fail in the task of sampling from the distribution of n indistinguishable photons after a propagation in a m-mode optical interferometer. In this context, in the absence of classical algorithms able to simulate efficiently multi-photon interference, the validation of Boson Sampling is still an open problem. Here we investigate a novel approach to Boson Sampling validation based on statistical properties of correlation functions. In particular we discuss its feasibility in actual proof-of-principle experiments. Furthermore we provide an extensive study of the physical resources required to validate experiments, investigating also the role of bosonic bunching in high-dimensional applications. Our investigation confirms the goodness of the validation protocol, paving the way to use this toolbox for the validation of Boson Sampling devices.
Entangled photons generation is an interesting field of research, since progress in this area will directly affect the development of photonic quantum technologies, including quantum computing, simulation and sensing. Several methods have been sifted to increase the performances of entangled photon sources and the integrated optics approach represents a promising strategy. In particular, integrated waveguide sources represent a robust tool, thanks to their stability and the enhancement of nonlinear light-crystal interaction provided by waveguide field confinement.
Here, we show the versatility of a hybrid approach, realizing an integrated optical source for the generation of entangled photon-pairs at telecom wavelength. The nonlinear active medium used is lithium niobate, while the routing and manipulation of the generated signal is performed in aluminum-borosilicate glass photonic circuits. The system is composed of three cascaded devices. First, a balanced directional coupler at the fundamental wavelength equally splits the pump in the lithium niobate waveguides, which generate single-photon pairs through type 0 spontaneous parametric down-conversion process. A third chip, encompassing directional couplers and waveplates, closes the interferometer and recombines the generated photons, thus giving access to different quantum states of light: path-entangled or polarization-entangled states. A thermal phase shifter, which controls the relative phase between the interferometer arms, gives an additional degree of freedom for engineering the output state of the presented photon pairs source. All these components are entirely fabricated by femtosecond laser micromachining, a direct and very versatile technique that allows to process different kind of materials and realize high quality optical circuits.
The investigation of multi-photon quantum interference in symmetric multi-port splitters has both fundamental and applicative interest. Destructive quantum interference in devices with specific symmetry leads to the suppression of a large number of possible output states, generalizing the Hong-Ou-Mandel effect; simple suppression laws have been developed for interferometers implementing the Fourier or the Hadamard transform over the modes. In fact, these enhanced interference features in the output distribution can be used to assess the indistinguishability of single-photon sources, and symmetric interferometers have been envisaged as benchmark or validation devices for Boson-Sampling machines. In this work we devise an innovative approach to implement symmetric multi-mode interferometers that realize the Fourier and Hadamard transform over the optical modes, exploiting integrated waveguide circuits. Our design is based on the optical implementations of the Fast-Fourier and Fast-Hadamard transform algorithms, and exploits a novel three-dimensional layout which is made possible by the unique capabilities of femtosecond laser waveguide writing. We fabricate devices with m = 4 and m = 8 modes and we let two identical photons evolve in the circuit. By characterizing the coincidence output distribution we are able to observe experimentally the known suppression laws for the output states. In particular, we characterize the robustness of this approach to assess the photons' indistinguishability and to rule out alternative non-quantum states of light. The reported results pave the way to the adoption of symmetric multiport interferometers as pivotal tools in the diagnostics and certification of quantum photonic platforms.
We experimentally observed in an optical setup and using full tomography process the so-called weak non-Markovian dynamics of a qubit . This was done implementing the collisional model proposed in  to investigate the non- Markovian dynamics of an open quantum system interacting with a carefully controlled environment state. We also observed the transition from weak to strong (essentially) non-Markovianity. In our all-optical setup, a single photon system, initially entangled in polarization with an ancilla, is made to interact with a sequence of liquid crystal retarders driven by proper electric pulses, which simulates the environment. Depending on how the voltage is applied on each liquid crystal, it will work as a half-wave plate with different orientations. Then, by changing properly the parameters of the qubit-environment interactions, the system dynamics can suffer a transition from weak to strong non-Markovianity. In the strong regime, the full reconstruction of the entangled state was made by single entanglement witness between system and ancilla, showing a backflow of information, while, in the weak regime, given the contractive unital map feature, we can only measure the dynamics by a full process tomography analysis, searching for the violation of the divisibility completely positive map criterion, what was done successfully.
Integrated photonic circuits with many input and output modes are essential in applications ranging from conventional optical telecommunication networks, to the elaboration of photonic qubits in the integrated quantum information framework. In particular, the latter field has been object in the recent years of an increasing interest: the compactness and phase stability of integrated waveguide circuits are enabling experiments unconceivable with bulk-optics set-ups. Linear photonic devices for quantum information are based on quantum and classical interference effects: the desired circuit operation can be achieved only with tight fabrication control on both power repartition in splitting elements and phase retardance in the various paths. Here we report on a novel three-dimensional circuit architecture, made possible by the unique capabilities of femtosecond laser waveguide writing, which enables us to realize integrated multimode devices implementing arbitrary linear transformations. Networks of cascaded directional couplers can be built with independent control on the splitting ratios and the phase shifts in each branch. In detail, we show an arbitrarily designed 5×5 integrated interferometer: characterization with one- and two-photon experiments confirms the accuracy of our fabrication technique. We exploit the fabricated circuit to implement a small instance of the boson-sampling experiments with up to three photons, which is one of the most promising approaches to realize phenomena hard to simulate with classical computers. We will further show how, by studying classical and quantum interference in many random multimode circuits, we may gain deeper insight into the bosonic coalescence phenomenon.
The application of integrated photonic technologies to quantum optics has recently enabled a wealth of
breakthrough experiments in several quantum information areas. In particular, femtosecond laser written
optical circuits revealed to be the ideal tool for investigating the features of polarization encoded qubits.
However, the difficulty of integrating half and quarter wave plates in such circuits avoids the possibility to
perform arbitrary rotations of the polarization state of photons on chip.
Femtosecond laser written waveguides intrinsically exhibit a certain degree of birefringence and thus they
could be exploited as integrated waveplates. In practice, the direction of the birefringence axes of the
waveguides is the same of the propagation direction of the writing femtosecond laser beam, namely
perpendicular to the substrate surface. Its fine rotation in a controlled fashion, preserving the accuracy of the
positioning of the laser focal spot required by the fabrication process, is extremely challenging. In order to
achieve this goal, we combine a high NA (1.4) focusing objective partially filled with a reduced diameter
writing beam. In this way, the translation of the beam with respect to the objective center produces a rotation
of the focusing direction, without altering the focal spot position. With this method we are able to tilt the
birefringence axes of the waveguides up to 45°, and thus to use them as integrated light polarization rotators.
In order to demonstrate the effectiveness of these components, we developed a fully integrated device capable
to perform the quantum tomography of an arbitrary two-photon polarization state.
The rotational properties of a light beam are controlled by its spin and orbital angular momentum (SAM and OAM). The q-plate, a liquid crystal device that can give rise to a coupling of these two quantities, was introduced a few years ago, leading to several applications in classical and quantum photonics. Very recently, in particular, a specific kind of q-plate was used to generate rotational-invariant states of single photons, which were then employed for performing a demonstration of quantum key distribution without the need for establishing a common reference frame between the transmitting and the receiving units. This result may find applications in future satellite-based quantum communication. By a similar approach, photonic states having a strongly enhanced rotational sensitivity, as opposed to rotational invariance, can be generated by using q-plates with very high topological charge. Photons in these states can be obtained starting from light having a uniform linear polarization and, after a physical rotation, can be converted back into light having uniformly linear polarization. As a result, one obtains linearly polarized light whose polarization plane rotates by an angle that is proportional to the angle of physical rotation between the generation and detection stages, with a very large proportionality constant. This effect of rotational amplification, which we named “photonic gear”, leads to a sort of “super-resolved Malus’ law”, potentially useful for measuring mechanical angles with very high precision.
Qudits, the d-dimensional extension of qubits, open new perspectives in several fields, from fundamental quantum mechanics to quantum cryptography. Although photon polarization is a privileged choice for qubits encoding, it is not suitable for the physical realization of qudits. However, in order to realize multidimensional quantum systems, other degrees of freedom of single photons such as path or orbital angular momentum are available. When two or more degrees of freedom are exploited simultaneously we refer to "hybrid encoding". It is possible for instance to encode information in a four dimensional (ququart) hybrid space spanned by polarization and a bidimensional orbital angular momentum subspace of a single photon. Here we present how high dimensional hybrid systems can be exploited to overcome a major limitation of quantum communication: the need of a shared reference frame. Indeed the joint action of polarization and orbital angular momentum of hybrid ququarts can be exploited to realize quantum communication without a shared reference frame. We experimentally showed that, by using a proper subspace of hybrid ququart space, it is possible to perform any quantum communication protocol and violate CHSH inequalities without any information about the reference frame orientation of the two parties (except the direction of propagation of the photons). Such feature could find application in satellite based communication schemes.
The orbital angular momentum carried by single photons represents a promising resource in the quantum information
field. In this paper we report some recent results regarding the adoption of higher dimensional quantum
states encoded in the polarization and orbital angular momentum for quantum information and cryptographic
The ability to manipulate quantum states of light by integrated devices may open new perspectives both for
fundamental tests of quantum mechanics and for novel technological applications. The technology for handling
polarization-encoded qubits, the most commonly adopted approach, was still missing in quantum optical circuits
until the ultrafast laser writing (ULW) technique was adopted for the first time to realize integrated devices able
to support and manipulate polarization encoded qubits.1 Thanks to this method, polarization dependent and independent
devices can be realized. In particular the maintenance of polarization entanglement was demonstrated
in a balanced polarization independent integrated beam splitter1 and an integrated CNOT gate for polarization
qubits was realized and carachterized.2 We also exploited integrated optics for quantum simulation tasks: by
adopting the ULW technique an integrated quantum walk circuit was realized3 and, for the first time, we investigate
how the particle statistics, either bosonic or fermionic, influences a two-particle discrete quantum walk.
Such experiment has been realized by adopting two-photon entangled states and an array of integrated symmetric
directional couplers. The polarization entanglement was exploited to simulate the bunching-antibunching
feature of non interacting bosons and fermions. To this scope a novel three-dimensional geometry for the waveguide
circuit is introduced, which allows accurate polarization independent behaviour, maintaining a remarkable
control on both phase and balancement of the directional couplers.
Photonics is a powerful framework for testing in experiments quantum information ideas, which promise significant
advantages in computation, cryptography, measurement and simulation tasks. Linear optics is in principle
sufficient to achieve universal quantum computation, but stability requirements become severe when experiments
have to be implemented with bulk components. Integrated photonic circuits, on the contrary, due to
their compact monolithic structure, easily overcome stability and size limitations of bench-top setups. Anyway,
for quantum information applications, they have been operated so far only with fixed polarization states of the
photons. On the other hand, many important quantum information processes and sources of entangled photon
states are based on the polarization degree of freedom. In our work we demonstrate femtosecond laser fabrication
of novel integrated components which are able to support and manipulate polarization entangled photons. The
low birefringence and the unique possibility of engineering three-dimensional circuit layouts, allow femtosecond
laser written waveguides to be eminently suited for quantum optics applications. In fact, this technology enables
to realize polarization insensitive circuits which have been employed for entangled Bell state filtration and implementation
of discrete quantum walk of entangled photons. Polarization sensitive devices can also be fabricated,
such as partially polarizing directional couplers, which have enabled on-chip integration of quantum logic gates
reaching high fidelity operation.
In the optical sensing context one of the main challenge is to design and implement novel techniques of sensing optimized
to work in a lossy scenario, in which effects of environmental disturbances can destroy the benefits deriving from the
adoption of quantum resources. Here we describe the experimental implementation of a protocol based on the process
of optical parametric amplification to boost interferometry sensitivity in the presence of losses in a minimally invasive
scenario. By performing the amplification process on a microscopic probe after the interaction with the sample, we can
beat the losses detrimental effect on the phase measurement which affects the single photon state after its interaction with
the sample, and thus improve the achievable sensitivity.
The emerging strategy to overcome the limitations of bulk quantum optics consists of taking advantage of the
robustness and compactness achievable by the integrated waveguide technology. Here we report the realization
of a directional coupler, fabricated by femtosecond laser waveguide writing, acting as an integrated beam splitter
able to support polarization encoded qubits. This maskless and single step technique allows to realize circular
transverse waveguide profiles able to support the propagation of Gaussian modes with any polarization state.
Using this device, we demonstrate the quantum interference with polarization entangled states.
In this work we present the realization of multiphoton quantum states, obtained by optical parametric amplification,
and we investigate their perspectives and possible applications. The multiphoton quantum states are
generated by a quantum-injected optical parametric amplifier (QI-OPA) seeded by a single-photon belonging
to an EPR entangled pair. The entanglement between the micro-macroscopic photon system is experimentally
demonstrated, and the possible applications of the macro-qubits states are presented and discussed.
The orbital angular momentum carried by single photons represents a promising resource in the quantum information
field. In this paper we report the characterization in the quantum regime of a recently introduced
optical device, known as q-plate. Exploiting the spin-orbit coupling that takes place in the q-plate, it is possible
to transfer coherently the information from the polarization to the orbital angular momentum degree of freedom,
and viceversa. Hence the q-plate provides a reliable bi-directional interface between polarization and orbital
angular momentum. As a first paradigmatic demonstration of the q-plate properties, we have carried out the
first experimental Hong-Ou-mandel effect purely observed in the orbital angular momentum degree of freedom.
In the present work we propose to realize a macroscopic light-matter entangled state, obtained by the interaction
of a multiphoton quantum superposition with a BEC system. The multiphoton quantum state is generated
by a quantum-injected optical parametric amplifier (QI-OPA) seeded by a single-photon belonging to an EPR
entangled pair and interacts with a Mirror-BEC shaped as a Bragg interference structure. The overall process
will realize an entangled macroscopic quantum superposition involving a "microscopic" single-photon state of
polarization and the coherent "macroscopic" displacement of the BEC structure acting in space-like separated
distant places. This hybrid photonic-atomic system could open new perspectives on the possibility of coupling
the amplified radiation with an atomic ensemble, a Bose-Einstein condensate, in order to implement innovative
quantum interface between light and matter.
We investigate the multiphoton states generated by high-gain optical parametric amplification of a single injected
photon, polarization encoded as a "qubit". The experiment configuration exploits the optimal phase-covariant
cloning in the high gain regime. The interference fringe pattern showing the non local transfer of coherence
between the injected qubit and the mesoscopic amplified output field involving up to 4000 photons has been
investigated. A probabilistic new method to extract full information about the multiparticle output wavefunction
has been implemented. This technique can be adopted to test the entanglement between a microscopic system
and a macro one.