Author Correction: All-optical implementation of collision-based evolutions of open quantum systems.

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

Experimental Investigation of Superdiffusion via Coherent Disordered Quantum Walks.

Many disordered systems show a superdiffusive dynamics, intermediate between the diffusive one, typical of a classical stochastic process, and the so-called ballistic behavior, which is generally expected for the spreading in a quantum process. We have experimentally investigated the superdiffusive behavior of a quantum walk, 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 quantum walk evolution.

Experimental Investigation of Quantum Decay at Short, Intermediate, and Long Times via Integrated Photonics.

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.

All-optical implementation of collision-based evolutions of open quantum systems.

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.

Stimulated emission tomography: beyond polarization.

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

First observation of the quantized exciton-polariton field and effect of interactions on a single polariton.

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.

Experimental nonlocality-based network diagnostics of multipartite entangled 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 illustrate the effectiveness of our proposal by characterizing a quantum resource engineered combining two-photon hyperentanglement and photonic-chip technology. Our approach opens up future studies on 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.

Learning an unknown transformation via a genetic approach.

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.

Photonic simulation of entanglement growth and engineering after a spin chain quench.

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.

Experimental Detection of Quantum Channel Capacities.

We present an efficient experimental procedure that certifies nonvanishing 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 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 σ_{x}⊗σ_{x}, σ_{y}⊗σ_{y}, and σ_{z}⊗σ_{z}.

Suppression law of quantum states in a 3D photonic fast Fourier transform chip.

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.

Path-polarization hyperentangled and cluster states of photons on a chip.

Encoding many qubits in different degrees of freedom (DOFs) of single photons is one of the routes toward enlarging the Hilbert space spanned by a photonic quantum state. Hyperentangled photon states (that is, states showing entanglement in multiple DOFs) have demonstrated significant implications for both fundamental physics tests and quantum communication and computation. Increasing the number of qubits of photonic experiments requires miniaturization and integration of the basic elements, and functions to guarantee the setup stability, which motivates the development of technologies allowing the precise control of different photonic DOFs on a chip. We demonstrate the contextual use of path and polarization qubits propagating within an integrated quantum circuit. We tested the properties of four-qubit linear cluster states built on both DOFs, and we exploited them to perform the Grover's search algorithm according to the one-way quantum computation model. Our results pave the way toward the full integration on a chip of hybrid multi-qubit multiphoton states.

Experimental observation of weak non-Markovianity.

Non-Markovianity has recently attracted large interest due to significant advances in its characterization and its exploitation for quantum information processing. However, up to now, only non-Markovian regimes featuring environment to system backflow of information (strong non-Markovianity) have been experimentally simulated. In this work, using an all-optical setup we simulate and observe the so-called weak non-Markovian dynamics. Through full process tomography, we experimentally demonstrate that the dynamics of a qubit can be non-Markovian despite an always increasing correlation between the system and its environment which, in our case, denotes no information backflow. We also show the transition from the weak to the strong regime by changing a single parameter in the environmental state, leading us to a better understanding of the fundamental features of non-Markovianity.

Experimental scattershot boson sampling.

Boson sampling is a computational task strongly believed to be hard for classical computers, but efficiently solvable by orchestrated bosonic interference in a specialized quantum computer. Current experimental schemes, however, are still insufficient for a convincing demonstration of the advantage of quantum over classical computation. A new variation of this task, scattershot boson sampling, leads to an exponential increase in speed of the quantum device, using a larger number of photon sources based on parametric down-conversion. This is achieved by having multiple heralded single photons being sent, shot by shot, into different random input ports of the interferometer. We report the first scattershot boson sampling experiments, where six different photon-pair sources are coupled to integrated photonic circuits. We use recently proposed statistical tools to analyze our experimental data, providing strong evidence that our photonic quantum simulator works as expected. This approach represents an important leap toward a convincing experimental demonstration of the quantum computational supremacy.

Experimental Generation of Robust Entanglement from Classical Correlations via Local Dissipation.

We experimentally show how classical correlations can be turned into quantum entanglement, via the presence of dissipation and the action of a CNOT gate. We first implement a simple two-qubit protocol in which entanglement production is not possible in the absence of such kind of noise, while it arises with its introduction, and is proportional to its amount. We then perform a more elaborate four-qubit experiment, by employing two hyperentangled photons initially carrying only classical correlations. We demonstrate a scheme where the entanglement is generated via local dissipation, with the advantage of being robust against local unitaries performed by an adversary.

Postselection-Loophole-Free Bell Test Over an Installed Optical Fiber Network.

Device-independent quantum communication will require a loophole-free violation of Bell inequalities. In typical scenarios where line of sight between the communicating parties is not available, it is convenient to use energy-time entangled photons due to intrinsic robustness while propagating over optical fibers. Here we show an energy-time Clauser-Horne-Shimony-Holt Bell inequality violation with two parties separated by 3.7 km over the deployed optical fiber network belonging to the University of Concepción in Chile. Remarkably, this is the first Bell violation with spatially separated parties that is free of the postselection loophole, which affected all previous in-field long-distance energy-time experiments. Our work takes a further step towards a fiber-based loophole-free Bell test, which is highly desired for secure quantum communication due to the widespread existing telecommunication infrastructure.

Particle statistics affects quantum decay and Fano interference.

Quantum mechanical decay, Fano interference, and bound states with energy in the continuum are ubiquitous phenomena in different areas of physics. Here we experimentally demonstrate that particle statistics strongly affects quantum mechanical decay in a multiparticle system. By considering propagation of two-photon states in engineered photonic lattices, we simulate quantum decay of two noninteracting particles in a multilevel Fano-Anderson model. Remarkably, when the system sustains a bound state in the continuum, fractional decay is observed for bosonic particles, but not for fermionic ones. Complete decay in the fermionic case arises because of the Pauli exclusion principle, which forbids the bound state to be occupied by the two fermions. Our experiment indicates that particle statistics can tune many-body quantum decay from fractional to complete.

Experimental on-demand recovery of entanglement by local operations within non-Markovian dynamics.

In many applications entanglement must be distributed through noisy communication channels that unavoidably degrade it. Entanglement cannot be generated by local operations and classical communication (LOCC), implying that once it has been distributed it is not possible to recreate it by LOCC. Recovery of entanglement by purely local control is however not forbidden in the presence of non-Markovian dynamics, and here we demonstrate in two all-optical experiments that such entanglement restoration can even be achieved on-demand. First, we implement an open-loop control scheme based on a purely local operation, without acquiring any information on the environment; then, we use a closed-loop scheme in which the environment is measured, the outcome controling the local operations on the system. The restored entanglement is a manifestation of "hidden" quantum correlations resumed by the local control. Relying on local control, both schemes improve the efficiency of entanglement sharing in distributed quantum networks.

Experimental linear-optics simulation of multipartite non-locality in the ground state of a quantum Ising ring.

Critical phenomena involve structural changes in the correlations of its constituents. Such changes can be reproduced and characterized in quantum simulators able to tackle medium-to-large-size systems. We demonstrate these concepts by engineering the ground state of a three-spin Ising ring by using a pair of entangled photons. The effect of a simulated magnetic field, leading to a critical modification of the correlations within the ring, is analysed by studying two- and three-spin entanglement. In particular, we connect the violation of a multipartite Bell inequality with the amount of tripartite entanglement in our ring.

Rotated waveplates in integrated waveguide optics.

Controlling and manipulating the polarization state of a light beam is crucial in applications ranging from optical sensing to optical communications, both in the classical and quantum regime, and ultimately whenever interference phenomena are to be exploited. In addition, many of these applications present severe requirements of phase stability and greatly benefit from a monolithic integrated-optics approach. However, integrated devices that allow arbitrary transformations of the polarization state are very difficult to produce with conventional lithographic technologies. Here we demonstrate waveguide-based optical waveplates, with arbitrarily rotated birefringence axis, fabricated by femtosecond laser pulses. To validate our approach, we exploit this component to realize a compact device for the quantum state tomography of two polarization-entangled photons. This work opens perspectives for integrated manipulation of polarization-encoded information with relevant applications ranging from integrated polarimetric sensing to quantum key distribution.