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We show experimentally that a dc-biased Josephson junction in series with two microwave resonators emits entangled beams of microwaves leaking out of the resonators. In the absence of a stationary phase reference for characterizing the entanglement of the outgoing beams, we measure second-order coherence functions for proving entanglement up to an emission rate of 2.5 billion photon pairs per second. The experimental results are found in quantitative agreement with theory, proving that the low frequency noise of the dc bias is the main limitation for the coherence time of the entangled beams. This agreement allows us to evaluate the entropy of entanglement of the resonators, and to identify the improvements that could bring this device closer to a useful bright source of entangled microwaves for quantum-technological applications.

Anyons, particles displaying a fractional exchange statistics intermediate between bosons and fermions, play a central role in the fractional quantum Hall effect and various spin lattice models, and have been proposed for topological quantum computing schemes due to their resilience to noise. Here we use parametric down-conversion in an integrated semiconductor chip to generate biphoton states simulating anyonic particle statistics, in a reconfigurable manner. Our scheme exploits the frequency entanglement of the photon pairs, which is directly controlled through the spatial shaping of the pump beam. These results, demonstrated at room temperature and telecom wavelength on a chip-integrated platform, pave the way to the practical implementation of quantum simulation tasks with tailored particle statistics., 8 pages

International audience; Photonic quantum technologies represent a promising platform for applications ranging from long-distance secure communications to the simulation of complex phenomena. Among the different material platforms, direct bandgap semiconductors offer a wide range of functionalities opening promising perspectives for the implementation of future quantum technologies. In this paper, we review our progress on the generation and manipulation of quantum states of light in nonlinear AlGaAs chips and their use in quantum networks.

Hybrid encoding of quantum information is a promising approach towards the realisation of optical quantum protocols. It combines advantages of continuous variables encoding, such as high efficiencies, with those of discrete variables, such as high fidelities. In particular, entangled hybrid states were shown to be a valuable ressource for quantum information protocols. In this work, we present a hybrid entanglement witness that can be implemented on currently available experiments and is robust to noise currently observed in quantum optical set-ups. The proposed witness is based on measurements of genuinely hybrid observables. The noise model we consider is general. It is formally characterised with Kraus operators since the considered hybrid system can be expressed in a finite dimension basis. A practical advantage of the witness is that it can be tested by measuring just a few experimentally available observables., Comment: 16 pages, 8 figures

In the late 1980's, Ou and Mandel experimentally observed signal beatings by performing a non-time-resolved coincidence detection of two photons having interfered in a balanced beam splitter [Phys. Rev. Lett 61, 54 (1988)]. In this work, we provide an alternative interpretation of the fringe pattern observed in this experiment as the direct measurement of the chronocyclic Wigner distribution of a frequency Schr\"odinger-cat-like state produced by local spectral filtering. Based on this analysis, we also study the time-resolved HOM experiment to measure such frequency state.

Encoding quantum information in continuous variables is intrinsically faulty. Nevertheless, redundant qubits can be used for error correction, as proposed by Gottesman, Kitaev and Preskill in Phys. Rev. A \textbf{64} 012310, (2001). We show how to experimentally implement this encoding using time-frequency continuous degrees of freedom of photon pairs produced by spontaneous parametric down conversion. We experimentally illustrate our results using an integrated AlGaAs photon pairs source. We show how single qubit gates can be implemented and finally propose a theoretical scheme for correcting errors in a circuit-like and in a measurement-based architecture.

High-dimensional entangled states of light provide novel possibilities for quantum information, from fundamental tests of quantum mechanics to enhanced computation and communication protocols. In this context, the frequency degree of freedom is particular attractive thanks to its robustness to propagation in optical fibers and its capability to convey large scale of quantum information into a single spatial mode. This provides a strong incentive for the development of efficient and scalable methods for the generation and the manipulation of frequency-encoded quantum states. Nonlinear parametric processes are powerful tools to generate such states, but up to now the manipulation of the generated frequency states has been carried out mostly by post-manipulation, which demands complex and bulk-like experimental setups. Direct production of on-demand frequency-states at the generation stage, and if possible using a chip-based source, is crucial in view of practical and scalable applications for quantum information technologies. Here we use an integrated semiconductor chip to engineer the wavefunction and exchange statistics of frequency-entangled photon pairs directly at the generation stage, without post-manipulation. Tuning the pump spatial intensity allows to produce frequency-anticorrelated, correlated and separable states, while tuning the spatial phase enables to switch between symmetric and antisymmetric spectral wavefunctions, leading respectively to bosonic and fermionic behaviors of the photons. We also demonstrate the generation of non-Gaussian entanglement in the continuous variables formed by the frequency and time degrees of freedom of the photon pairs. These results, obtained at room temperature and telecom wavelength, and with a chip-based source, open promising perspectives for the quantum simulation of fermionic problems with photons on an integrated platform, as well as for communication and computation protocols exploiting antisymmetric high-dimensional quantum states.

We introduce a quasi-probability phase space distribution with two pairs of azimuthal-angular coordinates. This representation is well adapted to describe quantum systems with discrete symmetry. Quantum error correction of states encoded in continuous variables using translationally invariant states is studied as an example of application. We also propose an experimental scheme for measuring such new distribution.

Quantum frequency combs are a useful resource for parallel quantum communication and processing, given the robustness and easy handling offered by the frequency degree of freedom. In this work, we propose a method to generate broadband biphoton frequency combs and control their symmetry under particle exchange, based on purely passive optical components, such as a cavity and an optical delay line. We experimentally demonstrate our method using an integrated AlGaAs semiconductor platform producing quantum frequency combs, working at room temperature and compliant with electrical injection. We show the generation and manipulation of biphoton frequency combs, spreading over more the 500 peaks. These results open interesting perspectives for the development of massively parallel and reconfigurable systems for complex quantum operations.

In the context of phase estimation with Gaussian states, we introduce a quantifiable definition of metrological advantage that takes into account thermal noise in the preparation procedure. For a broad set of states, \textit{isotropic non-pure Gaussian states}, we show that squeezing is not only necessary, but sufficient, to achieve metrological advantage. We interpret our results in the framework of resource theory, and discuss possible sources of advantage other than squeezing. Our work is a step towards using phase estimation with pure and mixed state to define and quantify nonclassicality. This work is complementary with studies that defines nonclassicality using quadrature displacement estimation., Changes to wording, figures replaced

International audience; When the coupling rate between two quantum systems becomes as large as their characteristic frequencies, it induces dramatic effects on their dynamics and even on the nature of their ground state. The case of a qubit coupled to a harmonic oscillator in this ultrastrong coupling regime has been investigated theoretically and experimentally. Here, we explore the case of two harmonic oscillators in the ultrastrong coupling regime. Probing the properties of their ground state remains out of reach in natural implementations. Therefore, we have realized an analog quantum simulation of this coupled system by dual frequency pumping a nonlinear superconducting circuit. The pump amplitudes directly tune the effective coupling rate. We observe spectroscopic signature of a mode hybridization that is characteristic of the ultrastrong coupling. We experimentally demonstrate a key property of the ground state of this simulated ultrastrong coupling between modes by observing simultaneous single- and two-mode squeezing of the radiated field below vacuum fluctuations.

The controllability of current quantum technologies allows to implement spin-boson models where two-photon couplings are the dominating terms of light-matter interaction. In this case, when the coupling strength becomes comparable with the characteristic frequencies, a spectral collapse can take place, i.e. the discrete system spectrum can collapse into a continuous band. Here, we analyze the thermodynamic limit of the two-photon Dicke model, which describes the interaction of an ensemble of qubits with a single bosonic mode. We find that there exists a parameter regime where two-photon interactions induce a superradiant phase transition, before the spectral collapse occurs. Furthermore, we extend the mean-field analysis by considering second-order quantum fluctuations terms, in order to analyze the low-energy spectrum and compare the critical behavior with the one-photon case., Minor changes to the text and equations, references added. 11 pages, 4 figures

Instantaneous quantum computing is a sub-universal quantum complexity class, whose circuits have proven to be hard to simulate classically in the Discrete-Variable (DV) realm. We extend this proof to the Continuous-Variable (CV) domain by using squeezed states and homodyne detection, and by exploring the properties of post-selected circuits. In order to treat post-selection in CVs we consider finitely-resolved homodyne detectors, corresponding to a realistic scheme based on discrete probability distributions of the measurement outcomes. The unavoidable errors stemming from the use of finitely squeezed states are suppressed through a qubit-into-oscillator GKP encoding of quantum information, which was previously shown to enable fault-tolerant CV quantum computation. Finally, we show that, in order to render post-selected computational classes in CVs meaningful, a logarithmic scaling of the squeezing parameter with the circuit size is necessary, translating into a polynomial scaling of the input energy., Published version

We introduce a cavity-optomechanical system where the temporal envelope of input/output pulses is controlled by an independent classical drive. We design protocols for quantum communication between distant mechanical resonators.

Using superconducting circuits, we present an experimental simulation of the ultrastrong coupling between two harmonic oscillators.

We propose a method that uses a superconducting architecture to simulate a time-dependent ultrastrong coupling between two bosonic fields. We show that the system emits microwave radiation with complex noise properties.

La dualite onde/particule se teste la plupart du temps a l’aide de photons uniques envoyes dans un interferometre de Mach-Zehnder equilibre. On peut alors observer des comportements consideres comme mutuellement exclusifs, a savoir ondulatoire (presence d’interferences) ou corpusculaire (absence d’interferences) selon la presence ou l’absence de la lame separatrice en sortie de l’interferometre. Nous presentons un nouveau type d’experience de complementarite dans laquelle cette lame separatrice est preparee dans une superposition coherente lui permettant d’etre a la fois presente et absente. Cette preparation est « activee » grâce a l’emploi de paires de photons intriques en polarisation. L’un des photons, dit test, est envoye dans l’interferometre et est detecte alors que son jumeau, dit corroborant, permet de determiner si un comportement de type ondulatoire, corpusculaire ou intermediaire a ete observe pour le photon test. En manipulant l’etat de polarisation du photon corroborant et la phase de l’interferometre du photon test, nous observons une transition continue entre aspects ondulatoire et corpusculaire, signature forte de la notion de complementarite introduite par Bohr et donc de la non exclusivite de ces comportements.

Complementarity, that is the ability of a quantum object to behave either as a particle or as a wave, is one of the most intriguing features of quantum mechanics. An exemplary Gedanken experiment, emphasizing such a measurement-dependent nature, was suggested by Wheeler using single photons. The subtleness of the idea lies in the fact that the output beam-splitter of a Mach-Zehnder interferometer is put in or removed after a photon has already entered the interferometer, thus performing a delayed test of the wave-particle complementary behavior. Recently, it was proposed that using a quantum analogue of the output beam-splitter would permit carrying out this type of test after the detection of the photon and observing wave-particle superposition. In this paper we describe an experimental demonstration of these predictions using another extraordinary property of quantum systems, entanglement. We use a pair of polarization entangled photons composed of one photon whose nature (wave or particle) is tested, and of a corroborative photon that allows determining which one, or both, of these two aspects is being tested. This corroborative photon infers the presence or absence of the beam-splitter and until it is measured, the beam-splitter is in a superposition of these two states, making it a quantum beam-splitter. When the quantum beam-splitter is in the state present or absent, the interferometer reveals the wave or particle nature of the test photon, respectively. Furthermore, by manipulating the corroborative photon, we can continuously morph, via entanglement, the test photon from wave to particle behavior even after it was detected. This result underlines the fact that a simple vision of light as a classical wave or a particle is inadequate., Comment: 8 Figures

We investigate the output generation of squeezed radiation of a cavity photon mode coupled to another off-resonant bosonic excitation. By modulating in time their linear interaction, we predict high degree of output squeezing when the dispersive ultrastrong coupling regime is achieved, i.e., when the interaction rate becomes comparable to the frequency of the lowest energy mode. Our work paves the way to squeezed light generation in frequency domains where the ultrastrong coupling is obtained, e.g., solid-state resonators in the GHz, THz and mid-IR spectral range., 6 pages, 2 figures

The ground state of a pair of ultrastrongly coupled bosonic modes is predicted to be a two-mode squeezed vacuum. However, the corresponding quantum correlations are currently unobservable in condensed matter where such a coupling can be reached, since it cannot be extracted from these systems. Here, we show that superconducting circuits can be used to perform an analog simulation of a system of two bosonic modes in regimes ranging from strong to ultrastrong coupling. More importantly, our quantum simulation setup enables us to detect output excitations that are related to the ground-state properties of the bosonic modes. We compute the emission spectra of this physical system and show that the produced state presents single- and two-mode squeezing simultaneously., Comment: 8 pages, 4 figures

Particle number fluctuations, no matter how small, are present in experimental set-ups. One should rigorously take these fluctuations into account, especially, for entanglement detection. In this context, we generalize the spin squeezing inequalities introduced by T\'oth et al. in Phys. Rev. Lett. 99, 250405 (2007). These new inequalities are fulfilled by all separable states even when the number of particle is not constant, and may present quantum fluctuations. These inequalities are useful for detecting entanglement in many-body systems when the super-selection rule does not apply, or when only a subspace of the total systems Hilbert space is considered. We also define general dichotomic observables for which we obtain a coordinate independent form of the generalized spin squeezing inequalities. We give an example where our generalized coordinate independent spin squeezing inequalities present a clear advantage over the original ones., Comment: 11 pages, 2 figures

We present a general strategy to derive entanglement criteria through a dichotomization procedure which consists of performing a mapping from qudits to qubits that preserves the separability of the parties and the SU(2) rotational invariance. Consequently, it is possible to apply the well-known positive partial transpose criterion to reveal the existence of quantum correlations between qudits. We discuss some examples of entangled states that are detected using the proposed strategy. Finally, we demonstrate, using our scheme, how some variance-based entanglement witnesses can be generalized from qubits to higher dimensional spin systems.

Reaching the strong coupling regime of light-matter interaction has led to an impressive development in fundamental quantum physics and applications to quantum information processing. Latests advances in different quantum technologies, like superconducting circuits or semiconductor quantum wells, show that the ultrastrong coupling regime (USC) can also be achieved, where novel physical phenomena and potential computational benefits have been predicted. Nevertheless, the lack of effective decoupling mechanism in this regime has so far hindered control and measurement processes. Here, we propose a method based on parity symmetry conservation that allows for the generation and reconstruction of arbitrary states in the ultrastrong coupling regime of light-matter interactions. Our protocol requires minimal external resources by making use of the coupling between the USC system and an ancillary two-level quantum system., Comment: Improved version. 9 pages, 5 figures

We provide a toolbox for continuous variables quantum state engineering and characterization of biphoton states produced by spontaneous parametric down conversion in a transverse pump configuration. We show that the control of the pump beam's incidence spot and angle corresponds to phase space displacements of conjugate collective continuous variables of the biphoton. In particular, we illustrate with numerical simulations on a semiconductor device how this technique can be used to engineer and characterize arbitrary states of the frequency and time degrees of freedom.

We present a theoretical proposal to couple a single Nitrogen-Vacancy (NV) center to a superconducting flux qubit (FQ) in the regime where both systems are off resonance. The coupling between both quantum devices is achieved through the strong driving of the flux qubit by a classical microwave field that creates dressed states with an experimentally controlled characteristic frequency. We discuss several applications such as controlling the NV center's state by manipulation of the flux qubit, performing the NV center full tomography and using the NV center as a quantum memory. The effect of decoherence and its consequences to the proposed applications are also analyzed. Our results provide a theoretical framework describing a promising hybrid system for quantum information processing, which combines the advantages of fast manipulation and long coherence times., Comment: 8 pages, 9 figures

The Leggett-Garg inequality is a widely used test of the "quantumness" of a system, and involves correlations between measurements realized at different times. According to its widespread interpretation, a violation of the Legget-Garg inequality disproofs macroscopic realism and non-invasiveness. Nevertheless, recent results point out that macroscopic realism is a model dependent notion and that one should always be able to attribute to invasiveness a violation of a Legget-Garg inequality. This opens some natural questions: how to provide such an attribution in a systematic way? How can apparent macroscopic realism violation be recast into a dimensional independent invasiveness model? The present work answers these questions by introducing an operational model where the effects of invasiveness are controllable through a parameter associated with what is called the {\it measurability} of the physical system. Such a parameter leads to different generalized measurements that can be associated with the dimensionality of a system, to measurement errors or to back action., Comment: 5 pages, 4 figures, published version

Binary quantum information can be fault tolerantly encoded in states defined in infinite dimensional Hilbert spaces. Such states define a computational basis, and permit a perfect equivalence between continuous and discrete universal operations. The drawback of this encoding is that the corresponding logical states are unphysical, meaning infinitely localized in phase space. We use the modular variables formalism to show that, in a number of protocols relevant for quantum information and for the realization of fundamental tests of quantum mechanics, it is possible to loosen the requirements on the logical subspace without jeopardizing their usefulness or their successful implementation. Such protocols involve measurements of appropriately chosen modular observables that permit the readout of the encoded discrete quantum information from the corresponding logical states. Finally, we demonstrate the experimental feasibility of our approach by applying it to the transverse degrees of freedom of single photons., Comment: 15 pages, 4 figures

Single photon interference due to passage through a periodic grating is considered in a novel proposal for processing D-dimensional quantum systems (quDits) encoded in the spatial degrees of freedom of light. We show that free space propagation naturally implements basic single quDit gates by means of the Talbot effect: an intricate time-space carpet of light in the near field diffraction regime. Adding a diagonal phase gate, we show that a complete set of single quDit gates can be implemented. We then introduce a spatially-dependent beam splitter that allows implementation of controlled operations between two quDits. A new form of universal quantum information processing can then be implemented with linear optics and ancilla photons. Though we consider photons, our scheme should be directly applicable to a number of other physical systems. Interpretation of the Talbot effect as a quantum logic operation provides a beautiful and interesting way to visualize quantum computation through wave propagation and interference., 11 pages, 8 figures

We give explicit expressions for canonical states labeling the vast majority of entanglement equivalent classes of symmetric states of qubits and efficient algorithms for reducing a given state to the representative of the class it belongs. This way, we achieve an almost complete classification under local unitary and local invertible transformations for symmetric states. The main tool is a technique introduced in this work, enabling to decompose in a unique way, spin symmetric states into a superposition of spin-$1/2$ coherent states. For the case of two qubits, the proposed decomposition reproduces the Schmidt decomposition and therefore, in the case of a higher number of qubits, can be considered as its generalization.

We propose a cavity quantum electrodynamics (CQED) experiment to test the violation of a Bell-type inequality using non-local mesoscopic states (NLMS). These states involve coherent field superpositions stored in two spatially-separated high-Q cavities. The inequality is expressed in terms of the measured Wigner function of the entangled two-field-mode system at four points in phase space, as proposed in [Banaszek and Wodkiewicz, Phys. Rev. Lett. 82, 2009 (1999)]. We examine the production of these entangled NLMS and the measurement of their Wigner function. The experiment involves circular Rydberg atoms and superconducting millimeter-wave cavities. We present a detailed numerical study of the optimal inequality violation and of the effect of decoherence. We discuss the range of experimental parameters making it possible to observe a locality violation and show that they correspond to realistic, albeit demanding, conditions.

Cavity QED is a versatile tool to explore small scale quantum information processing. Within this setting, we describe a particular protocol for implementing a Toffoli gate with Rydberg atoms and a cavity field. Our scheme uses both resonant and non resonant interactions, and in particular a cavity assisted atomic collision. The experimental feasibility of the protocol is carefully analyzed with the help of numerical simulations and takes into account the decoherence process. Moreover, we show that our protocol is optimal within the constraints imposed by the experimental setting.

Cavity quantum electrodynamics has already proven to be a system capable of demonstrating basic tools in quantum information theory. By combining these tools, we show how simple quantum information protocols could be implemented. We will focus on the examples of the Grover search algorithm and quantum cloning.

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.

The contextuality of quantum mechanics, i.e. the measurement outcome dependence upon previously made measurements, can be shown by the violation of inequalities based on measurements of well chosen observables. An important property of such observables is that their expectation value can be expressed in terms of probabilities of obtaining two exclusive outcomes. In order to satisfy this, inequalities have been constructed using either observables with a dichotomic spectrum or using periodic functions obtained from displacement operators in phase space. Here we identify the general conditions on the spectral decomposition of observables demonstrating state independent contextuality of quantum mechanics. As a consequence, our results not only unify existing strategies for maximal violation of state independent non-contextual inequalities but also lead to new scenarii enabling such violation. Among the consequences of our results is the impossibility of having a state independent maximal violation of non-contextuality in the Peres-Mermin scenario with discrete observables of odd dimensions., Comment: 6 pages

In quantum theory, observables with a continuous spectrum are known to be fundamentally different from those with a discrete and finite spectrum. While some fundamental tests and applications of quantum mechanics originally formulated for discrete variables have been translated to continuous ones, this is not the case in general. For instance, despite their importance, no experimental demonstration of nonlocality exists in the continuous variables regime. Attempts to bridge this gap and put continuous variables on a closer footing to discrete ones used dichotomization. However, this approach considers only discrete properties of the continuum, and its infinitesimal properties are not fully exploited. Here we show that it is possible to manipulate, detect and classify continuous variable states using observables with a continuous spectrum revealing properties and symmetries which are analogous to finite discrete systems. Our approach leads to an operational way to define and adapt, to arbitrary continuous quantum systems, quantum protocols and algorithms typical to discrete systems., Comment: 5 pages + Supplementary Information

We propose experimental methods to engineer reservoirs at arbitrary temperature which are feasible with current technology. Our results generalize to mixed states the possibility of quantum state engineering through controlled decoherence. Finite-temperature engineered reservoirs can lead to the experimental observation of thermal entanglement---the appearance and increase of entanglement with temperature---to the study of the dependence of finite-time disentanglement and revival with temperature, quantum thermodynamical effects, and others, enlarging the comprehension of temperature-dependent entanglement properties. Our proposal is discussed in detail in two model systems, consisting of different modes of a single photon and a trapped-ion system.

The Clauser-Horne-Shimony and Holt inequality applies when measurements with binary outcomes are performed on physical systems under the assumption of local realism. Testing such inequalities in the quantum realm usually involves either measurements of two--valued quantum observables or pre-defining a context dependent binning procedure. Here we establish the conditions to test the Clauser-Horne-Shimony and Holt inequality using any quantum observable. Our result applies to observables with an arbitrary spectrum and no prior knowledge of their underlying Hilbert space's dimension is required. Finally, we demonstrate the proposed general measurement strategy, that can be seen as positive operator valued measurements performed on the system, using the formalism of modular variables applied to the transverse degrees of freedom of single photons., Comment: 10 pages, 4 figures, including a new Sec. 4

We report a quantum delayed-choice experiment based on entanglement, enabling to continuously morph single photons behavior from wave-like to particle-like, illustrating the inadequacy of a naive wave or particle description of light.

Summary form only given. In these last years, a great deal of effort has been devoted to the miniaturization of quantum information technology on semiconductor chips. In the context of photon pair sources, the bi-exciton cascade of a quantum dot and the four-wave mixing in Silicon waveguides have been used to demonstrate the generation of entangled states. Spontaneous parametric down-conversion in III-V semiconductor waveguides combines the advantages of room temperature and telecom wavelength operation, while keeping open the possibility of electrically pumping of the device. Here we present a source consisting of a multilayer AlGaAs waveguide grown on a GaAs substrate and then chemically etched to achieve lateral confinement in a ridge. The structure design is such that a pump beam (around 775 nm), impinging on the surface of the waveguide with an incidence angle θ, generates two counterpropagating orthogonally polarized beams (around 1550 nm). The waveguide core is surrounded by distributed Bragg reflectors to enhance the pump field. We demonstrate the direct emission of polarization entangled photons by pumping the device with two symmetric angles of incidence corresponding to frequency degeneracy and performing a quantum tomography measurement. Most common entanglement witnesses are satisfied and a raw fidelity of 0.8 to the Bell state ( Hν +eiφ vx ) is obtained. A theoretical model, taking into account the experimental parameters, provides ways to understand and control the amount of entanglement.These results open the route to the demonstration of other interesting features of our device such as the generation of hyper-entangled states via the control of the frequency correlation degree through the spatial and spectral pump beam profile, leading to a new generation of completely integrated devices for quantum information.

The Hong-Ou-Mandel (HOM) experiment was a benchmark in quantum optics, evidencing the quantum nature of the photon. In order to go deeper, and obtain the complete information about the quantum state of a system, for instance, composed by photons, the direct measurement or reconstruction of the Wigner function or other quasi--probability distribution in phase space is necessary. In the present paper, we show that a simple modification in the well-known HOM experiment provides the direct measurement of the Wigner function. We apply our results to a widely used quantum optics system, consisting of the biphoton generated in the parametric down conversion process. In this approach, a negative value of the Wigner function is a sufficient condition for non-gaussian entanglement between two photons. In the general case, the Wigner function provides all the required information to infer entanglement using well known necessary and sufficient criteria. We analyze our results using two examples of parametric down conversion processes taken from recent experiments. The present work offers a new vision of the HOM experiment that further develops its possibilities to realize fundamental tests of quantum mechanics involving decoherence and entanglement using simple optical set-ups., 5 pages, 2 figures plus supplementary information; submitted; comments welcome

International audience; We demonstrate the generation of polarization-entangled photon pairs at room temperature and telecom wavelength in a AlGaAs semiconductor waveguide. The source is based on spontaneous parametric down conversion with a counterpropagating phase-matching scheme. The quality of the two-photon state is assessed by the reconstruction of the density matrix giving a raw fidelity to a Bell state of 0.83; a theoretical model, taking into account the experimental parameters, provides ways to understand and control the amount of entanglement. Its compatibility with electrical injection, together with the high versatility of the generated two-photon state, make this source an attractive candidate for completely integrated quantum photonics devices.

In recent years, great efforts have been devoted to the miniaturization of quantum information technology on semiconductor chips. In the context of photon pair sources, the bi-exciton cascade of a quantum dot and the four wave mixing in a Silicon waveguide have been used to demonstrate the generation of entangled states. Spontaneous parametric down-conversion in III-V semiconductor waveguides combines the advantages of room temperature and telecom wavelength operation, while keeping open the possibility of electrically pumping of the device. Here we present a source consisting of a multilayer AlGaAs waveguide grown on a GaAs substrate and then chemically etched to achieve lateral confinement in a ridge. The structure design is such that a pump beam (around 759 nm), impinging on the waveguide surface with an incidence angle θ generates two counterpropagating orthogonally polarized beams (around 1518 nm). The waveguide core is surrounded by distributed Bragg reectors to enhance the pump field within the device. We demonstrate the direct emission of polarization entangled photons by pumping the device at two symmetric angles of incidence corresponding to frequency degeneracy and performing a quantum tomography measurement. Most common entanglement witnesses are satisfied and a raw fidelity of F = 0:86 to a Bell state is obtained. These results open the route to the demonstration of other interesting features of our device such as the generation of hyper-entangled states via the control of the frequency correlation degree through the spatial and spectral pump beam profile, leading to a new generation of completely integrated devices for quantum information.

The contextuality of quantum mechanics can be shown by the violation of inequalities based on measurements of well chosen observables. These inequalities have been designed separately for both discrete and continuous variables. Here we unify both strategies by introducing general conditions to demonstrate the contextuality of quantum mechanics from measurements of observables of arbitrary dimensions. Among the consequences of our results is the impossibility of having a maximal violation of contextuality in the Peres-Mermin scenario with discrete observables of odd dimensions. In addition, we show how to construct a large class of observables with a continuous spectrum enabling the realization of contextuality tests both in the Gaussian and non-Gaussian regimes.

The Leggett-Garg inequality is a widely used test of the "quantumness" of a system, and involves correlations between measurements realized at different times. According to its widespread interpretation, a violation of the Legget-Garg inequality disproves macroscopic realism and non-invasiveness. Nevertheless, recent results point out that macroscopic realism is a model dependent notion and that one should always be able to attribute to invasiveness a violation of a Legget-Garg inequality. This opens some natural questions: how to provide such an attribution in a systematic way? How can apparent macroscopic realism violation be recast into a dimensional independent invasiveness model? The present work answers these questions by introducing an operational model where the effects of invasiveness are controllable through a parameter associated with what is called the measurability of the physical system. Such a parameter leads to different generalized measurements that can be associated with the dimensionality of a system, to measurement errors or to back action.

We operate a superconducting quantum processor consisting of two tunable transmon qubits coupled by a swapping interaction, and equipped with nondestructive single-shot readout of the two qubits. With this processor, we run the Grover search algorithm among four objects and find that the correct answer is retrieved after a single run with a success probability between $0.52$ and $0.67$, which is significantly larger than the $0.25$ achieved with a classical algorithm. This constitutes a proof of concept for the quantum speed-up of electrical quantum processors.

We study the interaction of an intense classical field with a two-level system coupled to a bosonic quantized field. We focus on the regime where the classical field and the two-level system characteristic frequencies are the same, while the quantized mode is set off resonance with both. We show that a parameter governing the dynamics of the system is the ratio between the classical field's intensity and the quantized mode detuning. Depending on this parameter, multiple excitations can be created in the quantized mode in a single cycle of the two-level system. Examples of physical setups allowing for the application of the presented ideas are superconducting circuits in strip-line resonators, laser cooled trapped ions, and neutral atoms coupled to the quantized field of a cavity. We focus on the latter in order to show that, with realistic experimental parameters, it is possible to generate up to four photons in a single Rabi cycle.