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Abstract Quantum engineering now allows to design and construct multi-qubit states in a range of physical systems. These states are typically quite complex in nature, with disparate, but relevant properties that include both single and multi-qubit coherences and even entanglement. All these properties can be assessed by reconstructing the density matrix of those states—but the large parameter space can mean physical insight of the nature of those states and their coherence can be hard to achieve. Here, we explore how the Wigner function of a multipartite system and its visualization provides rich information on the nature of the state, not only at illustrative level but also at the quantitative level. We test our tools in a photonic architecture making use of the multiple degrees of freedom of two photons. Graphic abstract

Developing strategies to effectively discriminate between different quantum states is a fundamental issue in quantum information and communication. The actual realization of generally optimal protocols in this task is often limited by the need of supplemental resources and very complex receivers. We have experimentally implemented two discrimination schemes in a minimum-error scenario based on a receiver featured by a network structure and a dynamical processing of information. The first protocol implemented in our experiment, directly inspired to a recent theoretical proposal, achieves binary optimal discrimination, while the second one provides a novel approach to multi-state quantum discrimination, relying on the dynamical features of the network-like receiver. This strategy exploits the arrival time degree of freedom as an encoding variable, achieving optimal results, without the need for supplemental systems or devices. Our results further reveal the potential of dynamical approaches to quantum state discrimination tasks, providing a possible starting point for efficient alternatives to current experimental strategies.

We show an experimental procedure to certify the classical capacity for noisy qubit channels. The method makes use of a fixed bipartite entangled state, where the system qubit is sent to the channel input and the set of local measurements $\sigma_{x}\otimes\sigma_{x}$, $\sigma_{y}\otimes\sigma_{y}$ and $\sigma_{z}\otimes\sigma_{z}$ is performed at the channel output and the ancilla qubit, thus without resorting to full quantum process tomography. The witness to the classical capacity is then achieved by reconstructing sets of conditional probabilities, noise deconvolution, and classical optimization of the pertaining mutual information. The performance of the method to provide lower bounds to the classical capacity is tested by a two-photon polarization entangled state in Pauli channels and amplitude damping channels. The measured lower bounds to the channels are in high agreement with the simulated data, which take into account both the experimental entanglement fidelity $F=0.979\pm 0.011$ of the input state and the systematic experimental imperfections., Comment: 9 pages, 3 figures, 3 tables. Improved version, with tables of experimental conditional probabilities

We experimentally implemented a controllable inhomogenous Quantum Walk evolution of two photon states. Through the imposition of suitable disorder configurations, we observed an enhance-ment in quantum correlations of the system, compared to the ordered case.

The presence of disorder and inhomogeneities in quantum networks has often been unexpectedly beneficial for both quantum and classical resources. Here, we experimentally realize a controllable inhomogenous Quantum Walk dynamics, which can be exploited to investigate the effect of coherent disorder on the quantum correlations between two indistinguishable photons. Through the imposition of suitable disorder configurations, we observe two photon states which exhibit an enhancement in the quantum correlations between two modes of the network, compared to the case of an ordered Quantum Walk. Different configurations of disorder can steer the system towards different realizations of such an enhancement, thus allowing spatial and temporal manipulation of quantum correlations., Comment: 11 pages, 12 figures

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

We design a quantum probing protocol using quantum walks to investigate the quantum information spreading pattern. We employ quantum Fisher information as a figure of merit to quantify extractable information about an unknown parameter encoded within the quantum walk evolution. Although the approach is universal, we focus on the coherent static and dynamic disorder to investigate anomalous and classical transport as well as Anderson localization. We provide a feasible experimental strategy to implement, in principle, the quantum probing protocol based on the quantum Fisher information using a Mach–Zehnder-like interferometric setup. Our results show that a quantum walk can be considered as a readout device of information about defects and perturbations occurring in complex networks, both classical and quantum.

Whereas classical physics generally predicts an exponential trend for the temporal decay of an unstable state, quantum mechanics provides a rather different description. The decay is initially quadratic, while at very large times it follows a power-law. Actually, the latter regime has never been observed experimentally. Here we employ arrays of femtosecond-laser-written optical waveguides to optically realize quantum systems where a discrete state is coupled to and can decay into a continuum. The transverse optical modes represent distinct quantum states of the photon and the temporal evolution of the system is mapped into the longitudinal propagation coordinate. By injecting laser light in the fabricated structures, and by imaging with high dynamic range the scattered light from above, we are able to observe experimentally different decay regimes, including the power-law tail. This process can be viewed as the quantum simulation of a quantum decay phenomenon.

Sources of entangled photons are cornerstones of photonic quantum technologies, providing the basic resources for a wide range of quantum protocols for computing, simulation and sensing. A typical technique to generate entangled photon pairs exploits spontaneous parametric down conversion (SPDC) in non-linear crystals. In this context, an integrated-optics approach based on non-linear waveguides [1] can boost source brightness due to the enhanced mode confinement, and can take great advantage from the unique compactness and stability of on-chip devices. However, integrated devices are often specialized to produce a given quantum state.

The decay of an unstable system is usually described by an exponential law. Quantum mechanics predicts strong deviations of the survival probability from the exponential: Indeed, the decay is initially quadratic, while at very large times it follows a power law, with superimposed oscillations. The latter regime is particularly elusive and difficult to observe. Here we employ arrays of single-mode optical waveguides, fabricated by femtosecond laser direct inscription, to implement quantum systems where a discrete state is coupled and can decay into a continuum. The optical modes correspond to distinct quantum states of the photon, and the temporal evolution of the quantum system is mapped into the spatial propagation coordinate. By injecting coherent light states in the fabricated photonic structures and by measuring a small scattered fraction of such light with an unprecedented dynamic range, we are able to experimentally observe not only the exponential decay regime, but also the quadratic Zeno region and the power-law decay at long evolution times.

A novel bulk optics scheme for quantum walks is presented. It consists of a one-dimensional lattice built on two concatenated displaced Sagnac interferometers that make it possible to reproduce all the possible trajectories of an optical quantum walk. Because of the closed loop configuration, the interferometric structure is intrinsically stable in phase. Moreover, the lattice structure is highly configurable, as any phase component perceived by the walker is accessible, and finally, all output modes can be measured at any step of the quantum walk evolution. We report here on the experimental implementation of ordered and disordered quantum walks., This manuscript is organized in 5 sections, containing 8 pages and 7 figures

Many disordered systems show a superdiffusive dynamics, intermediate between the diffusive one, typical of a classical stochastic process, and the so called ballistic behaviour, which is generally expected for the spreading in a quantum process. We have experimentally investigated the superdiffusive behaviour of a quantum walk (QW), whose dynamics can be related to energy transport phenomena, with a resolution which is high enough to clearly distinguish between different disorder regimes. By our experimental setup, the region between ballistic and diffusive spreading can be effectively scanned by suitably setting few degrees of freedom and without applying any decoherence to the QW evolution., Comment: 5 pages, 5 figures + supplementary material

We present a bulk-optics setup for discrete quantum walks, based on a novel multipass displaced Sagnac geometry. It is phase stable, reconfigurable and allows to meausure the output radiation at each step. The experimental results of both ordered and disordered one-particle evolutions are reported.

A compact, robust and high quality on-chip source of entangled photons pair in telecom wavelength is presented. The entangled output state can be changed by means of the chip reconfigurability and its hybrid structure.

Waveguide arrays, fabricated by femtosecond laser pulses and excited by coherent light, are used to study quantum decay phenomena. By tailoring the system properties, we observe different regimes including quadratic Zeno and power-law decay.

We investigate the emergence of Quantum Darwinism in a photonic cluster as simulator of interactions between a quantum system and its environment. We demonstrate experimentally the effect of correlations in the emergence of objective reality.

We present a new optical scheme enabling the implementation of highly stable and configurable non-Markovian dynamics. Here one photon qubit can circulate in a multipass bulk geometry consisting of two concatenated Sagnac interferometers to simulate the so called collisional model, where the system interacts at discrete times with a vacuum environment. We show the optical features of our apparatus and three different implementations of it, replicating a pure Markovian scenario and two non-Markovian ones, where we quantify the information backflow by tracking the evolution of the initial entanglement between the system photon and an ancillary one., This document is organized in 5 sections, containing 10 pages and 7 figures

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.

Landauer’s principle introduces a symmetry between computational and physical processes: erasure of information, a logically irreversible operation, must be underlain by an irreversible transformation dissipating energy. Monitoring micro- and nano-systems needs to enter into the energetic balance of their control; hence, finding the ultimate limits is instrumental to the development of future thermal machines operating at the quantum level. We report on the experimental investigation of a lower bound to the irreversible entropy associated to generalized quantum measurements on a quantum bit. We adopted a quantum photonics gate to implement a device interpolating from the weakly disturbing to the fully invasive and maximally informative regime. Our experiment prompted us to introduce a bound taking into account both the classical result of the measurement and the outcoming quantum state; unlike previous investigation, our entropic bound is based uniquely on measurable quantities. Our results highlight what insights the information-theoretic approach provides on building blocks of quantum information processors. A lower bound for the thermodynamic cost of quantum measurements can be found from non-thermodynamic quantities. Modern classical and quantum devices can be used to explore the fundamental limits of computation, such as the energy required to measure or erase information. Luca Mancino and collaborators in Italy and the United Kingdom have demonstrated the evaluation of a lower limit on irreversible thermodynamic entropy generated during a quantum measurement. In general, thermodynamic quantities are difficult to measure but the authors' bound is calculated using information obtained from standard quantum optical measurements. Mancino et al. find that although their bound does not constrain the entropy tightly it does reflect how the experimental parameters affect the entropic cost of the measurements. This demonstrates the potential for using information-theoretic quantities to gain insight into quantum thermodynamics.

We demonstrate the generation of states hyperentangled in polarization and path by non-degenerate spontaneous down conversion. We characterize them by quantum state tomography and stimulated emission tomography.

Polaritons reach the quantum limit, providing a new and promising platform of strongly coherent and interacting particles., Polaritons are quasi-particles that originate from the coupling of light with matter and that demonstrate quantum phenomena at the many-particle mesoscopic level, such as Bose-Einstein condensation and superfluidity. A highly sought and long-time missing feature of polaritons is a genuine quantum manifestation of their dynamics at the single-particle level. Although they are conceptually perceived as entangled states and theoretical proposals abound for an explicit manifestation of their single-particle properties, so far their behavior has remained fully accounted for by classical and mean-field theories. We report the first experimental demonstration of a genuinely quantum state of the microcavity polariton field, by swapping a photon for a polariton in a two-photon entangled state generated by parametric downconversion. When bringing this single-polariton quantum state in contact with a polariton condensate, we observe a disentangling with the external photon. This manifestation of a polariton quantum state involving a single quantum unlocks new possibilities for quantum information processing with interacting bosons.

In this work we demonstrate the use of stimulated emission tomography to characterize a hyper-entangled state generated by spontaneous parametric down-conversion in a CW-pumped source. In particular, we consider the generation of hyper-entangled states consisting of photon pairs entangled in polarisation and path. These results extend the capability of stimulated emission tomography beyond the polarisation degree of freedom, and demonstrate the use of this technique to study states in higher dimension Hilbert spaces.

We report on an experimental assessment of the emergence of Quantum Darwinism (QD) from engineered open-system dynamics. We use a photonic hyperentangled source of graph states to address the effects that correlations among the elements of a multi-party environment have on the establishment of objective reality ensuing the quantum-to-classical transition. Besides embodying one of the first experimental efforts towards the characterization of QD, our work illustrates the non-trivial consequences that multipartite entanglement and, in turn, the possibility of having environment-to-system back-action have on the features of the QD framework., Comment: 5 pages, 5 figures, Revtex4-1

The time evolution of quantum many-body systems is one of the most important processes for benchmarking quantum simulators. The most curious feature of such dynamics is the growth of quantum entanglement to an amount proportional to the system size (volume law) even when interactions are local. This phenomenon has great ramifications for fundamental aspects, while its optimisation clearly has an impact on technology (e.g., for on-chip quantum networking). Here we use an integrated photonic chip with a circuit-based approach to simulate the dynamics of a spin chain and maximise the entanglement generation. The resulting entanglement is certified by constructing a second chip, which measures the entanglement between multiple distant pairs of simulated spins, as well as the block entanglement entropy. This is the first photonic simulation and optimisation of the extensive growth of entanglement in a spin chain, and opens up the use of photonic circuits for optimising quantum devices., The complete maximisation of the entanglement between two complementary blocks of spins due to the dynamics of spin chains remains to be observed. Here, Pitsios et al. simulate such dynamics by propagating single photons in an integrated photonic circuit.

The study of the evolution of quantum states performed with photonic techniques, commonly requires the use of complex interferometric schemes [1]. Here we present a novel setup based on multipass bulk interference that allows to recreate and measure different kinds of quantum state evolutions, passing from sequential maps to quantum walks.

Quantum networks of growing complexity play a key role as resources for quantum computation; the ability to identify the quality of their internal correlations will play a crucial role in addressing the building stage of such states. We introduce a novel diagnostic scheme for multipartite networks of entangled particles, aimed at assessing the quality of the gates used for the engineering of their state. Using the information gathered from a set of suitably chosen multiparticle Bell tests, we identify conditions bounding the quality of the entangled bonds among the elements of a register. We demonstrate the effectiveness, flexibility, and diagnostic power of the proposed methodology by characterizing a quantum resource engineered combining two-photon hyperentanglement and photonic-chip technology. Our approach is feasible for medium-sized networks due to the intrinsically modular nature of cluster states, and paves the way to section-by-section analysis of larger photonics resources.

The relation between the theory of entanglement and thermodynamics is very tight: a thermodynamic theory of quantum entanglement, as well as the establishment of rigorous formal connections between the laws of thermodynamics and the phenomenology of entanglement are currently open areas of investigation. In this quest, an interesting problem is embodied by the role played by entanglement in processes of work extraction from a working medium embodied by quantum information carriers. In this work, we experimentally address the question "Is there any intrinsic advantage for work extraction given by the use of an entangled working medium?". By addressing work-extraction protocols based on a mechanism intimately linked to the paradigm of Maxwell's daemon, and implementing suitably designed multi-photon optical interferometers, we demonstrate experimentally the intrinsic advantages for such tasks provided by bipartite and genuine multipartite entanglement. We highlight the unique nature of such tests by comparing their performance to standard tests for the inseparability of multi-photon state resources. Our work contributes strongly to the ongoing efforts in establishing photonic systems as a platform for experiments for information thermodynamics.

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.

Femtosecond laser microfabrication has emerged in the last decade as a powerful technique for direct inscription of low loss optical waveguides in practically any transparent dielectric substrate, showing outstanding versatility. Prototyping of new devices is made rapid, cheap and easy: optical circuits are written directly buried in the substrate, using the laser beam as an optical pen, without any need of costly masks as required by conventional photolithography. Many proof-of-principle demonstrations of integrated optics can be obtained, including splitters, directional couplers, and Mach-Zehnder interferometers. Actually, the road towards applications has just been opened, and the unique capabilities of femtosecond laser micromachining will enable achievements inconceivable with other technologies. In this work, the femtosecond laser fabrication technique is discussed, together with its application to the realization of integrated photonic quantum circuits.

We present an effcient experimental procedure that certifies non vanishing quantum capacities for qubit noisy channels. Our method is based on the use of a fixed bipartite entangled state, where the system qubit is sent to the channel input. A particular set of local measurements is performed at the channel output and the ancilla qubit mode, obtaining lower bounds to the quantum capacities for any unknown channel with no need of a quantum process tomography. The entangled qubits have a Bell state configuration and are encoded in photon polarization. The lower bounds are found by estimating the Shannon and von Neumann entropies at the output using an optimized basis, whose statistics is obtained by measuring only the three observables $\sigma_{x}\otimes\sigma_{x}$, $\sigma_{y}\otimes\sigma_{y}$ and $\sigma_{z}\otimes\sigma_{z}$., Comment: 5 pages and 3 figures in the principal article, and 4 pages in the supplementary material

We report a bulk optics experiment demonstrating the possibility of restoring the entanglement distribution through noisy quantum channels by inserting a suitable unitary operation (filter) in the middle of the transmission process. We focus on two relevant classes of single-qubit channels consisting in repeated applications of rotated phase damping or rotated amplitude damping maps, both modeling the combined Hamiltonian and dissipative dynamics of the polarization state of single photons. Our results show that interposing a unitary filter between two noisy channels can significantly improve entanglement transmission. This proof-of-principle demonstration could be generalized to many other physical scenarios where entanglement-breaking communication lines may be amended by unitary filters., Comment: 5 pages, 4 figures (three of them containing two internal images) and 1 table

Photonic circuits represent a promising platform to perform quantum simulation of several different physical phenomena. Indeed, large progresses have been achieved in the last few years due to the technological advances enabled by integrated photonics, which allowed to achieve a significant increase in the size of the implemented systems. Notable examples of observed phenomena in integrated circuits include Anderson localization [1] and transport mechanisms [2].

The distribution of entangled quantum systems among two or more nodes of a network is a key task at the basis of quantum communication, quantum computation, and quantum cryptography. Unfortunately, the transmission lines used in this procedure can introduce so many perturbations and so much noise in the transmitted signal that they prevent the possibility of restoring quantum correlations in the received messages either by means of encoding optimization or by exploiting local operations and classical communication. In this work we present a procedure which allows one to improve the performance of some of these channels. The mechanism underpinning this result is a protocol which we dub cut and paste, as it consists in extracting and reshuffling the subcomponents of these communication lines, which finally succeed in correcting each other. The proof of this counterintuitive phenomenon, while improving our theoretical understanding of quantum entanglement, also has a direct application in the realization of quantum information networks based on imperfect and highly noisy communication lines. A quantum optics experiment, based on the transmission of single-photon polarization states, is also presented which provides a proof-of-principle test of the proposed protocol.

Recent developments in integrated photonics technology are opening the way to the fabrication of complex linear optical interferometers. The application of this platform is ubiquitous in quantum information science, from quantum simulation to quantum metrology, including the quest for quantum supremacy via the boson sampling problem. Within these contexts, the capability to learn efficiently the unitary operation of the implemented interferometers becomes a crucial requirement. In this letter we develop a reconstruction algorithm based on a genetic approach, which can be adopted as a tool to characterize an unknown linear optical network. We report an experimental test of the described method by performing the reconstruction of a 7-mode interferometer implemented via the femtosecond laser writing technique. Further applications of genetic approaches can be found in other contexts, such as quantum metrology or learning unknown general Hamiltonian evolutions., Comment: 5 pages, 3 figures + 3 pages, 1 figure Supplementary Information

Photon entanglement is at the basis of many protocols in photonic quantum technologies, from quantum computing to simulation and sensing. The generation of entangled photons in integrated waveguides is particularly advantageous due to the enhanced stability and more efficient nonlinear interaction. Here we realize an integrated source of entangled wavelength-degenerate photons based on the hybrid interfacing of photonic circuits in different materials, all inscribed by femtosecond laser pulses. We show that our source, based on spontaneous parametric down-conversion at the telecom wavelength, gives access to different classes of output states, allowing us to switch from path-entangled to polarization-entangled states with net visibilities above 0.92 for all selected combinations of integrated devices. (C) 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Cluster states are the fundamental resource for the one-way model of quantum computation. In this paper we show the realization of a two-photon four-qubit cluster state. The qubits are encoded in the polarization and the linear momentum of the particles. By using this state we realized two important quantum algorithms, namely the Grover's search and the Deutsch's algorithm.

Four-qubit cluster states of two photons entangled in polarization and linear momentum have been used to realize a complete set of single qubit rotations and the C-NOT gate for equatorial qubits with high values of fidelity. By the computational equivalence of the two degrees of freedom our result demonstrate the suitability of two photon cluster states for rapid and efficient one-way quantum computing., RevTex4, 4 pages, 3 figures

Our paper [Phys. Rev. A 86, 032325 (2012)], setting forth a previously unknown connection between the Bennett 1992 protocol and a Bell inequality, has recently received a Comment [Phys. Rev. A 93, 066303 (2016)] about a possible flaw in its potential device-independent (DI) implementation. We point the authors of the Comment to prior works showing that what they assume to be specific to our protocol's DI implementation is actually a standard assumption in DI quantum key distribution. Therefore there is no need to revise any of the conclusions drawn in Lucamarini et al. [Phys. Rev. A 86, 032325 (2012)].

The identification of phenomena able to pinpoint quantum interference is attracting large interest. Indeed, a generalization of the Hong–Ou–Mandel effect valid for any number of photons and optical modes would represent an important leap ahead both from a fundamental perspective and for practical applications, such as certification of photonic quantum devices, whose computational speedup is expected to depend critically on multi-particle interference. Quantum distinctive features have been predicted for many particles injected into multimode interferometers implementing the Fourier transform over the optical modes. Here we develop a scalable approach for the implementation of the fast Fourier transform algorithm using three-dimensional photonic integrated interferometers, fabricated via femtosecond laser writing technique. We observe the suppression law for a large number of output states with four- and eight-mode optical circuits: the experimental results demonstrate genuine quantum interference between the injected photons, thus offering a powerful tool for diagnostic of photonic platforms., Computational speedup in photonic quantum devices depends on multi-particle interference, which must be certified through known benchmark algorithms. Here, to this end, the authors develop a scalable approach for the implementation of the fast Fourier transform algorithm in 3D photonic integrated interferometers.