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Quantum information systems are on a path to vastly exceed the complexity of any classical device. The number of entangled qubits in quantum devices is rapidly increasing and the information required to fully describe these systems scales exponentially with qubit number. This scaling is the key benefit of quantum systems, however it also presents a severe challenge. To characterize such systems typically requires an exponentially long sequence of different measurements, becoming highly resource demanding for large numbers of qubits. Here we propose a novel and scalable method to characterize quantum systems, where the complexity of the measurement process only scales linearly with the number of qubits. We experimentally demonstrate an integrated photonic chip capable of measuring two- and three-photon quantum states with reconstruction fidelity of 99.67%., 21 pages, 9 figures (includes supplementary material)

The femtosecond laser direct-writing (FLDW) of waveguide circuits in glasses has seen interest from a number of fields over the previous 20 years. It has evolved from a curiosity to a viable platform for the rapid prototyping of small scale circuits. The field of quantum information science has exploited this capability and in the process advanced the fabrication technique. In this review the technological aspects of the laser inscription method relevant to quantum information science will be discussed. A range of demonstrations which have been enabled by laser written circuits will be outlined; these include novel circuits, simulations, photon sources and detection. This places the FLDW technique among the few integrated optical platforms to have produced individually every component required for scalable quantum computation.

Multipartite entangled states like the W-class are of growing interest since they exhibit a variety of possible applications ranging from quantum computation to genuine random number generation. Here, we present a universal setup to generate high-order single photon W-states based on three-dimensional integrated-photonic waveguide structures. Additionally, we present a novel method to characterize the device's unitary by means of classical light only.

© 2017 IEEE. We formulate a method of quantum tomography that scales linearly with the number of photons and involves only one optical transformation. We demonstrate it experimentally for two-photon entangled states using a special photonic chip.

Single-photon W-states — coherent superpositions of all qubits with equal probability amplitudes — involving up to 16 spatial modes are generated by means of evanescently-coupled waveguide technology. A scheme capable of exploiting the maximal entanglement of W-states is proposed for the efficient generation of random numbers.

We report on the experimental observation of Bloch Oscillations of nonlocal quantum states. Our on-chip photonic lattice could serve as a platform for quantum simulation of the dynamics of bosonic, anyonic and fermionic particles.

In this work we experimentally demonstrate the realization of the discrete fractional Fourier transforms (DFrFT) in both the classical and quantum realm. Our approach is fully integrated and free of bulk optical components.

We report on our latest findings on photonic Quantum Walks (QW) of entangled particles in several quantum transport regimes as for instance in photonic Bloch lattices or disordered lattices. Furthermore, the discrete fractional Fourier transform of quantum states is presented in the context of QWs.

The key requirement for harnessing the quantum properties of light is the capability to detect and count individual photons. Of particular interest are photon-number-resolving detectors, which allow one to determine whether a state of light is classical or genuinely quantum. Existing schemes for addressing this challenge rely on a proportional conversion of photons to electrons. As such, they are capable of correctly characterizing small photon fluxes, yet are limited by uncertainties in the conversion rate. In this work, we employ a divide-and-conquer approach to infallibly discerning non-classicality of states of light. This is achieved by transforming the incident fields into uniform spatial distributions that readily lend themselves for characterization by standard on-off detectors. Since the exact statistics of the light stream in multiplexed on-off detectors are click statistics, our technique is freely scalable to accommodate–in principle–arbitrarily large photon fluxes. Our experiments pave the way towards genuine integrated photon-number-resolving detection for advanced on-chip photonic quantum networks.

Evanescent coupled waveguides could be used to build multipartite inferometeros, which create an optical quantum state generator. The characterization of these integrated photonic devices needs a large effort and experimental expertise. We develop a method to reduce the measurement steps rapidly by using classical laser light. We show the application of this technique on a laser written W-state generator of the order N = 8.

In this work we demonstrate, theoretically and experimentally, that two-photon probability amplitudes describing propagation of light in any two-photon state are governed by an evolution equation identical to a 2D tight-binding equation.

We experimentally demonstrate a fully integrated photon-counting device based on a divide-and-conquer technique using linear optics in combination with standard on-off detectors.

Transport phenomena on a quantum scale appear in a variety of systems, ranging from photosynthetic complexes to engineered quantum devices. It has been predicted that the efficiency of quantum transport can be enhanced through dynamic interaction between the system and a noisy environment. We report the first experimental demonstration of such environment-assisted quantum transport, using an engineered network of laser-written waveguides, with relative energies and inter-waveguide couplings tailored to yield the desired Hamiltonian. Controllable decoherence is simulated via broadening the bandwidth of the input illumination, yielding a significant increase in transport efficiency relative to the narrowband case. We show integrated optics to be suitable for simulating specific target Hamiltonians as well as open quantum systems with controllable loss and decoherence., Comment: 6 pages, 3 figures

Bloch Oscillations (BOs) of quantum particles manifest themselves as periodic spreading and re-localization of the associated wave functions when traversing lattice potentials subject to external gradient forces. Albeit BOs are deeply rooted into the very foundations of quantum mechanics, all experimental observations of this phenomenon so far have only contemplated dynamics of one or two particles initially prepared in separable local states, which is well described by classical wave physics. Evidently, a more general description of genuinely quantum BOs will be achieved upon excitation of a Bloch-oscillator lattice system by nonlocal states, that is, containing correlations in contradiction with local realism. Here we report the first experimental observation of BOs of two-particle Einstein-Podolsky-Rosen states (EPR), whose associated N-particle wave functions are nonlocal by nature. The time evolution of two-photon EPR states in Bloch-oscillators, whether symmetric, antisymmetric or partially symmetric, reveals unexpected transitions from particle antibunching to bunching. Consequently, the initial state can be tailored to produce spatial correlations akin to bosons, fermions or anyons. These results pave the way for a wider class of photonic quantum simulators., Comment: 21 pages, 6 figures

We experimentally demonstrate a method for integrated-optical generation of two-photon Einstein-Podolsky-Rosen states featuring arbitrary symmetries. In our setting, we employ detuned directional couplers to impose a freely tailorable phase between the two modes of the state. Our results allow to mimic the quantum random walk statistics of bosons, fermions, and anyons, particles with fractional exchange statistics.

We measure the next-nearest-neighbour coupling in an array of coupled optical waveguides directly via an integrated eigenmode interferometer. In contrast to light propagation experiments, the technique is insensitive to nearest-neighbour dynamics. Our results show that second-order coupling in a linear configuration can be suppressed well below the level expected from the exponential decay of the guided modes., Comment: Accepted by Applied Physics Letters. After publication, it will be found at http://scitation.aip.org/content/aip/journal/apl

Bloch oscillations of quantum particles manifest themselves as periodic spreading and relocalization of the associated wave functions when traversing lattice potentials subject to external gradient forces. Albeit this phenomenon is deeply rooted into the very foundations of quantum mechanics, all experimental observations so far have only contemplated dynamics of one and two particles initially prepared in separable local states. Evidently, a more general description of genuinely quantum Bloch oscillations will be achieved on excitation of a Bloch oscillator by nonlocal states. Here we report the observation of Bloch oscillations of two-particle N00N states, and discuss the nonlocality on the ground of Bell-like inequalities. The time evolution of two-photon N00N states in Bloch oscillators, whether symmetric, antisymmetric or partially symmetric, reveals transitions from particle antibunching to bunching. Consequently, the initial states can be tailored to produce spatial correlations akin to those of bosons, fermions and anyons, presenting potential applications in photonic quantum simulation., Bloch oscillations consist of periodic spreading and relocalization of particle wave functions, but have been so far observed only in separable states. Here the authors observe them for two-photon N00N states in integrated photonic circuits, revealing transitions from particle bunching to anitbunching.

We report on the experimental realization of quantum and classical discrete fractional Fourier transforms using photonic lattices. Our approach is fully integrated and free of bulk optical components.

We introduce special photonic lattices where we can, in principle, selectively excite the constitutive quantum eigenstates. Hence, through the excitation of such systems with single-photon W-states we can readily generate entanglement of the so-called W-eigenstates.

We present arbitrary wave plate operations on-chip based on the reorientation of the waveguide’s optical axis caused by additional stress fields. A successful implementation of Hadamard and Pauli-X gates for quantum light is shown.

Chip-based photonic quantum computing is an emerging technology that promises much speedup over conventional computers at small integration volumes. Particular interest is thereby given to polarisation-encoded photonic qubits, and many protocols have been developed for this encoding. However, arbitrary wave plate operation on chip are not available so far, preventing from the implementation of integrated universal quantum computing algorithms. In our work we close this gap and present Hadamard, Pauli-X, and rotation gates of high fidelity for photonic polarisation qubits on chip by employing a reorientation of the optical axis of birefringent waveguides. The optical axis of the birefringent waveguide is rotated due to the impact of an artificial stress field created by an additional modification close to the waveguide. By adjusting this length of the defect along the waveguide, the retardation between ordinary and extraordinary field components is precisely tunable including half-wave plate and quarter-wave plate operations. Our approach demonstrates the full range control of orientation and strength of the induced birefringence and thus allows arbitrary wave plate operations without affecting the degree of polarisation or introducing additional losses to the waveguides. The implemented gates are tested with classical and quantum light.

We experimentally realize the generation of high-order photon encoded W-states involving up to 16 optical modes. Furthermore, we exploit the inherent probabilistic properties of these multipartite entangled W-states for generating genuine random numbers.

We introduce a new perfect state transfer protocol based on single-photon W-eigenstates of photonic lattices. Such W-eigenstates appear as impulse response of the system, e.g., when single photons are launched into single sites.

We report on integrated photonic quantum circuits using laser-written waveguides with complex three-dimensional waveguide architectures for using multiple degrees of freedom, such as diffraction control and birefringence.

We present Hadamard, Pauli-X, and rotation gates of high fidelity for photonic polarization qubits on chip by modifying the orientation of the optical axis and the birefringence’s strength of femtosecond laser-written waveguides.

We experimentally demonstrate the generation of high-order photon-encoded W-states involving up to 16 spatial optical modes. Additionally, we utilize the inherent probabilistic properties of these multipartite entangled W-states for the generation of genuine random numbers.

Quantum random walks of identical particles are ubiquitous in various fields of physics [1]. They give rise to particle number correlations which have been explored in several discrete systems [2; 3]. However, an essential property of all these quantum systems is their Hermiticity. Recently parity-time(PT)-symmetric systems [4] attracted much attention. The Hamiltonians of such systems are not necessarily Hermitian, yet they still can exhibit purely real eigenvalue spectra.

In this work, we show theoretically and experimentally that in certain parity-time (PT) symmetric systems both transport regimes coexist, however on different time scales. Our study was based on a PT-symmetric optical waveguide array exhibiting an alternating loss profile with homogeneous coupling between neighbouring waveguides, as indicated in Fig.1(a). Mathematically, the dynamics of such a structure can be described by a set of coupled equations, which read -i∂zan = αan + κbn-1 + κbn and -i∂tbn = βbn+κan+1 +κan. Here, an and bn represent the field amplitudes inside the lattice site, κ is the coupling coefficient, and z is the longitudinal propagation direction. The waveguides exhibit alternating, complex propagation constants which are denoted by the respective values of α and β.

Within all physical disciplines, it is accepted that wave transport is predetermined by the existence of disorder. In this vein, it is known that ballistic transport is possible only when a structure is ordered, and that disorder is crucial for diffusion or (Anderson-)localization to occur. As this commonly accepted picture is based on the very foundations of quantum mechanics where Hermiticity of the Hamiltonian is naturally assumed, the question arises whether these concepts of transport hold true within the more general context of non-Hermitian systems. Here we demonstrate theoretically and experimentally that in ordered time-independent -symmetric systems, which are symmetric under space-time reflection, wave transport can undergo a sudden change from ballistic to diffusive after a specific point in time. This transition as well as the diffusive transport in general is impossible in Hermitian systems in the absence of disorder. In contrast, we find that this transition depends only on the degree of dissipation.

A novel approach to investigate the dynamics of indistinguishable particles in non-Hermitian lattice systems exhibiting loss is presented. Especially analyzed are two-particle dynamics in quasi-parity-time-symmetric systems for a variety of input states.

Over the last 20 years quantum walks (QWs) have gained increasing interest in the field of quantum information science and processing. In contrast to classical walkers, quantum objects exhibit intrinsic properties like non-locality and non-classical many-particle correlations, which renders QWs a versatile tool for quantum simulation and computation as well as for a deeper understanding of genuine quantum mechanics. Since they are highly controllable and hardly interact with their environment, photons seem to be ideally suited quantum walkers. In order to study and exploit photonic QWs, lattice structures that allow low loss coherent evolution of quantum states are demanded. Such requirements are perfectly met by integrated optical waveguide devices that additionally allow a substantial miniaturization of experimental settings. Moreover, by utilizing the femtosecond direct laser writing technique three-dimensional waveguide structures are capable of analyzing QWs also on higher dimensional geometries. In this context, advances and findings of photonic QWs are discussed in this review. Various concepts and experimental results are presented covering, such as different quantum transport regimes, the Boson sampling problem, and the discrete fractional quantum Fourier transform.

Universal quantum computers promise a dramatic speed-up over classical computers but a full-size realization remains challenging. However, intermediate quantum computational models have been proposed that are not universal, but can solve problems that are strongly believed to be classically hard. Aaronson and Arkhipov have shown that interference of single photons in random optical networks can solve the hard problem of sampling the bosonic output distribution which is directly connected to computing matrix permanents. Remarkably, this computation does not require measurement-based interactions or adaptive feed-forward techniques. Here we demonstrate this model of computation using high--quality laser--written integrated quantum networks that were designed to implement random unitary matrix transformations. We experimentally characterize the integrated devices using an in--situ reconstruction method and observe three-photon interference that leads to the boson-sampling output distribution. Our results set a benchmark for quantum computers, that hold the potential of outperforming conventional ones using only a few dozen photons and linear-optical elements.

In this work we experimentally demonstrate a fully integrated photon-counting device based on a divide-and-conquer technique using linear optics in combination with on-off detectors. Our scheme is based on click-counting statistics instead of photon-counting statistics.