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We present a new method for the spectral characterization of pulsed twin beam sources in the high gain regime, using cascaded stimulated emission. We show an implementation of this method for a ppKTP spontaneous parametric down-conversion source generating up to 60 photon pairs per pulse, and demonstrate excellent agreement between our experiments and our theory. This work enables the complete and accurate experimental characterization of high gain effects in parametric down conversion, including self and cross-phase modulation. Moreover, our theory allows the exploration of designs with the goal of improving the specifications of twin beam sources for application in quantum information, computation, sampling, and metrology.

A remarkable aspect of quantum theory is that certain measurement outcomes are entirely unpredictable to all possible observers. Such quantum events can be harnessed to generate numbers whose randomness is asserted based upon the underlying physical processes. We formally introduce, design and experimentally demonstrate an ultrafast optical quantum random number generator that uses a totally untrusted photonic source. While considering completely general quantum attacks, we certify and generate in real-time random numbers at a rate of $8.05\,$Gb/s with a rigorous security parameter of $10^{-10}$. Our security proof is entirely composable, thereby allowing the generated randomness to be utilised for arbitrary applications in cryptography and beyond. To our knowledge, this represents the fastest composably secure source of quantum random numbers ever reported., Comment: 37 pages, 7 figures. New substantial material has been added and the title was modified accordingly

Determining an unknown quantum state from an ensemble of identical systems is a fundamental, yet experimentally demanding, task in quantum science. Here we study the number of measurement bases needed to fully characterize an arbitrary multi-mode state containing a definite number of photons, or an arbitrary mixture of such states. We show this task can be achieved using only linear optics and photon counting, which yield a practical though non-universal set of projective measurements. We derive the minimum number of measurement settings required and numerically show that this lower bound is saturated with random linear optics configurations, such as when the corresponding unitary transformation is Haar-random. Furthermore, we show that for N photons, any unitary 2N-design can be used to derive an analytical, though non-optimal, state reconstruction protocol., Comment: 6+8 pages, 2 figures

Direct UV-written waveguides are fabricated in silica-on-silicon with birefringence of $(4.9 \pm 0.2) \times 10^{-4}$, much greater than previously reported in this platform. We show that these waveguides are suitable for the generation of heralded single photons at telecommunication wavelengths by spontaneous four-wave mixing. A pulsed pump field at 1060 nm generates pairs of photons in highly detuned, spectrally uncorrelated modes near 1550 nm and 800 nm. Waveguide-to-fiber coupling efficiencies of 78-91% are achieved for all fields. Waveguide birefringence is controlled through dopant concentration of $\mathrm{GeCl_4}$ and $\mathrm{BCl_3}$ using the flame hydrolysis deposition process. The technology provides a route towards the scalability of silica-on-silicon integrated components for photonic quantum experiments., Comment: 9 pages, 5 figures

We propose and demonstrate a modular architecture for reconfigurable on-chip linear-optical circuits. Each module contains 10 independent phase-controlled Mach-Zehnder interferometers; several such modules can be connected to each other to build large reconfigurable interferometers. With this architecture, large interferometers are easier to build and characterize than with traditional, bespoke, monolithic designs. We demonstrate our approach by fabricating three modules in the form of UV-written silica-on-silicon chips. We characterize these chips, connect them to each other, and implement a wide range of linear optical transformations. We envisage that this architecture will enable many future experiments in quantum optics., Comment: 5 pages, 3 figures

The current shift in the quantum optics community towards large-size experiments -- with many modes and photons -- necessitates new classical simulation techniques that go beyond the usual phase space formulation of quantum mechanics. To address this pressing demand we formulate linear quantum optics in the language of tensor network states. As a toy model, we extensively analyze the quantum and classical correlations of time-bin interference in a single fiber loop. We then generalize our results to more complex time-bin quantum setups and identify different classes of architectures for high-complexity and low-overhead boson sampling experiments.

We study the impact of experimental imperfections on a recently proposed protocol for performing quantum simulations of vibronic spectroscopy. Specifically, we propose a method for quantifying the impact of these imperfections, optimizing an experiment to account for them, and benchmarking the results against a classical simulation method. We illustrate our findings using a proof of principle experimental simulation of part of the vibronic spectrum of tropolone. Our findings will inform the design of future experiments aiming to simulate the spectra of large molecules beyond the reach of current classical computers., Comment: 11 pages

It has recently been shown that optical parametric oscillator (OPO) Ising machines, consisting of coupled optical pulses circulating in a cavity with parametric gain, can be used to probabilistically find low-energy states of Ising spin systems. In this work, we study optical Ising machines that operate under simplified Gaussian dynamics. We show that these dynamics are sufficient for reaching probabilities of success comparable to previous work. Based on this result, we propose modified optical Ising machines with simpler designs that do not use parametric gain yet achieve similar performance, thus suggesting a route to building much larger systems., Comment: 6 pages

We numerically investigate the implementation of Haar-random unitarity transformations and Fourier transformations in photonic devices consisting of beam splitters and phase shifters, which are used for integrated photonics implementations of boson sampling. The distribution of reflectivities required to implement an arbitrary unitary transformation is skewed towards low values, and this skew becomes stronger the larger the number of modes. A realistic implementation using Mach-Zehnder interferometers is incapable of doing this perfectly and thus has limited fidelity. We show that numerical optimisation and adding extra beam splitters to the network can help to restore fidelity.

Quantum interference of two independent particles in pure quantum states is fully described by the particles' distinguishability: the closer the particles are to being identical, the higher the degree of quantum interference. When more than two particles are involved, the situation becomes more complex and interference capability extends beyond pairwise distinguishability, taking on a surprisingly rich character. Here, we study many-particle interference using three photons. We show that the distinguishability between pairs of photons is not sufficient to fully describe the photons' behaviour in a scattering process, but that a collective phase, the triad phase, plays a role. We are able to explore the full parameter space of three-photon interference by generating heralded single photons and interfering them in a fibre tritter. Using multiple degrees of freedom - temporal delays and polarisation - we isolate three-photon interference from two-photon interference. Our experiment disproves the view that pairwise two-photon distinguishability uniquely determines the degree of non-classical many-particle interference.

Universal multiport interferometers, which can be programmed to implement any linear transformation between multiple channels, are emerging as a powerful tool for both classical and quantum photonics. These interferometers are typically composed of a regular mesh of beam splitters and phase shifters, allowing for straightforward fabrication using integrated photonic architectures and ready scalability. The current, standard design for universal multiport interferometers is based on work by Reck et al (Phys. Rev. Lett. 73, 58, 1994). We demonstrate a new design for universal multiport interferometers based on an alternative arrangement of beam splitters and phase shifters, which outperforms that by Reck et al. Our design occupies half the physical footprint of the Reck design and is significantly more robust to optical losses., Comment: 8 pages, 4 figures

Interference between independent single photons is perhaps the most fundamental interaction in quantum optics. It has become increasingly important as a tool for optical quantum information science, as one of the rudimentary quantum operations, together with photon detection, for generating entanglement between non-interacting particles. Despite this, demonstrations of large-scale photonic networks involving more than two independent sources of quantum light have been limited due to the difficulty in constructing large arrays of high-quality single photon sources. Here, we solve the key challenge, reporting a novel array of more than eighteen near-identical, low-loss, high-purity, heralded single photon sources achieved using spontaneous four-wave mixing (SFWM) on a silica chip. We verify source quality through a series of heralded Hong-Ou-Mandel experiments, and further report the experimental three-photon extension of the entire Hong-Ou-Mandel interference curves, which map out the interference landscape between three independent single photon sources for the first time., Comment: 16 pages including supplementary information

Alkali-filled hollow-core fibres are a promising medium for investigating light-matter interactions, especially at the single-photon level, due to the tight confinement of light and high optical depths achievable by light-induced atomic desorption. However, until now these large optical depths could only be generated for seconds at most once per day, severely limiting the practicality of the technology. Here we report the generation of highest observed transient ($>10^5$ for up to a minute) and highest observed persistent ($>2000$ for hours) optical depths of alkali vapours in a light-guiding geometry to date, using a caesium-filled Kagom\'e-type hollow-core photonic crystal fibre. Our results pave the way to light-matter interaction experiments in confined geometries requiring long operation times and large atomic number densities, such as generation of single-photon-level nonlinearities and development of single photon quantum memories., Comment: Author Accepted version

We report a comprehensive approach to analysing continuous-output photon detectors. We employ principal component analysis to maximise the information extracted, followed by a novel noise-tolerant parameterised approach to the tomography of PNRDs. We further propose a measure for rigorously quantifying a detector's photon-number-resolving capability. Our approach applies to all detectors with continuous-output signals. We illustrate our methods by applying them to experimental data obtained from a transition-edge sensor (TES) detector., Comment: 5 pages, 3 figures, also includes supplementary information

Quantum mechanics establishes the ultimate limit to the scaling of the precision on any parameter, by iden- tifying optimal probe states and measurements. While this paradigm is, at least in principle, adequate for the metrology of quantum channels involving the estimation of phase and loss parameters, we show that estimat- ing the loss parameters associated with a quantum channel and a realistic quantum detector are fundamentally different. While Fock states are provably optimal for the former, we identify a crossover in the nature of the optimal probe state for estimating detector imperfections as a function of the loss parameter. We provide explicit results for on-off and homodyne detectors, the most widely used detectors in quantum photonics technologies.

Phase estimation, at the heart of many quantum metrology and communication schemes, can be strongly affected by noise, whose amplitude may not be known, or might be subject to drift. Here, we investigate the joint estimation of a phase shift and the amplitude of phase diffusion, at the quantum limit. For several relevant instances, this multiparameter estimation problem can be effectively reshaped as a two-dimensional Hilbert space model, encompassing the description of an interferometer phase probed with relevant quantum states -- split single-photons, coherent states or N00N states. For these cases, we obtain a trade-off bound on the statistical variances for the joint estimation of phase and phase diffusion, as well as optimum measurement schemes. We use this bound to quantify the effectiveness of an actual experimental setup for joint parameter estimation for polarimetry. We conclude by discussing the form of the trade-off relations for more general states and measurements., Comment: Published in Nature Communications. Supplementary Information available at http://www.nature.com/ncomms/2014/140404/ncomms4532/extref/ncomms4532-s1.pdf

Quantum teleportation is a fundamental concept in quantum physics which now finds important applications at the heart of quantum technology including quantum relays, quantum repeaters and linear optics quantum computing (LOQC). Photonic implementations have largely focussed on achieving long distance teleportation due to its suitability for decoherence-free communication. Teleportation also plays a vital role in the scalability of photonic quantum computing, for which large linear optical networks will likely require an integrated architecture. Here we report the first demonstration of quantum teleportation in which all key parts - entanglement preparation, Bell-state analysis and quantum state tomography - are performed on a reconfigurable integrated photonic chip. We also show that a novel element-wise characterisation method is critical to mitigate component errors, a key technique which will become increasingly important as integrated circuits reach higher complexities necessary for quantum enhanced operation., Comment: Originally submitted version - refer to online journal for accepted manuscript; Nature Photonics (2014)

We develop a scheme for time-frequency encoded continuous-variable cluster-state quantum computing using quantum memories. In particular, we propose a method to produce, manipulate and measure 2D cluster states in a single spatial mode by exploiting the intrinsic time-frequency selectivity of Raman quantum memories. Time-frequency encoding enables the scheme to be extremely compact, requiring a number of memories that is a linear function of only the number of different frequencies in which the computational state is encoded, independent of its temporal duration. We therefore show that quantum memories can be a powerful component for scalable photonic quantum information processing architectures., Comment: 5 pages, 6 figures, and supplementary information. Updated to be consistent with published version

We present a practical method for active phase control on a photonic chip that has immediate applications in quantum photonics. Our approach uses strain-optic modification of the refractive index of individual waveguides, effected by a millimeter-scale mechanical actuator. The resulting phase change of propagating optical fields is rapid and polarization-dependent, enabling quantum applications that require active control and polarization encoding. We demonstrate strain-optic control of non-classical states of light in silica, showing the generation of 2-photon polarisation N00N states by manipulating Hong-Ou-Mandel interference. We also demonstrate switching times of a few microseconds, which are sufficient for silica-based feed-forward control of photonic quantum states., Comment: 7 pages, 5 figures. Updated to be consistent with published version

The integrated optical circuit is a promising architecture for the realization of complex quantum optical states and information networks. One element that is required for many of these applications is a high-efficiency photon detector capable of photon-number discrimination. We present an integrated photonic system in the telecom band at 1550 nm based on UV-written silica-on-silicon waveguides and modified transition-edge sensors capable of number resolution and over 40% efficiency. Exploiting the mode transmission failure of these devices, we multiplex three detectors in series to demonstrate a combined 79% +/- 2% detection efficiency with a single pass, and 88% +/- 3% at the operating wavelength of an on-chip terminal reflection grating. Furthermore, our optical measurements clearly demonstrate no significant unexplained loss in this system due to scattering or reflections. This waveguide and detector design therefore allows the placement of number-resolving single-photon detectors of predictable efficiency at arbitrary locations within a photonic circuit - a capability that offers great potential for many quantum optical applications.

We present a scheme for linear optical quantum computing using time-bin encoded qubits in a single spatial mode. We show methods for single-qubit operations and heralded controlled phase (CPhase) gates, providing a sufficient set of operations for universal quantum computing with the Knill-Laflamme-Milburn scheme. Our scheme is suited to available photonic devices and ideally allows arbitrary numbers of qubits to be encoded in the same spatial mode, demonstrating the potential for time-frequency modes to dramatically increase the quantum information capacity of fixed spatial resources. As a test of our scheme, we demonstrate the first entirely single spatial mode implementation of a two-qubit quantum gate and show its operation with an average fidelity of 0.84+-0.07., Comment: 5 pages, 4 figures. Updated to be consistent with the published version

A key obstacle to the experimental realization of many photonic quantum-enhanced technologies is the lack of low-loss sources of single photons in pure quantum states. We demonstrate a promising solution: generation of heralded single photons in a silica photonic chip by spontaneous four-wave mixing. A heralding efficiency of 40%, corresponding to a preparation efficiency of 80% accounting for detector performance, is achieved due to efficient coupling of the low-loss source to optical fibers. A single photon purity of 0.86 is measured from the source number statistics without filtering, and confirmed by direct measurement of the joint spectral intensity. We calculate that similar high-heralded-purity output can be obtained from visible to telecom spectral regions using this approach. On-chip silica sources can have immediate application in a wide range of single-photon quantum optics applications which employ silica photonics., Comment: 11 pages, 5 figures

Entanglement enhancement is a key task for quantum technologies. This operation performed on states produced by parametric down-conversion sources has been the object of several recent experimental investigations. In particular, conditional preparation by photon-subtraction has been shown to improve the entanglement of these states. Here we analyse the role played by non-Gaussian and Gaussian measurements in more general entanglement concentration operations performed on a pair of two-mode squeezed vacua. We find stringent requirements for achieving an improved entanglement enhancement by measuring jointly these two resource states., Comment: to appear on Quantum Measurements and Quantum Metrology

While universal quantum computers ideally solve problems such as factoring integers exponentially more efficiently than classical machines, the formidable challenges in building such devices motivate the demonstration of simpler, problem-specific algorithms that still promise a quantum speedup. We construct a quantum boson sampling machine (QBSM) to sample the output distribution resulting from the nonclassical interference of photons in an integrated photonic circuit, a problem thought to be exponentially hard to solve classically. Unlike universal quantum computation, boson sampling merely requires indistinguishable photons, linear state evolution, and detectors. We benchmark our QBSM with three and four photons and analyze sources of sampling inaccuracy. Our studies pave the way to larger devices that could offer the first definitive quantum-enhanced computation., Comment: Main text: 5 pages, 4 figures. Supp Info: 6 pages

The generation of large multiphoton quantum states - for applications in computing, metrology, and simulation - requires a network of high-efficiency quantum memories capable of storing broadband pulses. Integrating these memories into a fibre offers a number of advantages towards realising this goal: strong light-matter coupling at low powers, simplified alignment, and compatibility with existing photonic architectures. Here, we introduce a large-core kagome-structured hollow-core fibre as a suitable platform for an integrated fibre-based quantum memory with a warm atomic vapour. We demonstrate, for the first time, efficient optical pumping in a hollow-core photonic-crystal fibre with a warm atomic vapour, where (90 $\pm$ 1)% of atoms are prepared in the ground state. We measure high optical depths (3$\times 10^{4}$) and, also, narrow homogeneous linewidths that do not exhibit significant transit-time broadening. Our results establish that kagome fibres are suitable for implementing a broadband, room-temperature quantum memory., Comment: 10 pages, 4 figures

Increasing the complexity of quantum photonic devices is essential for many optical information processing applications to reach a regime beyond what can be classically simulated, and integrated photonics has emerged as a leading platform for achieving this. Here, we demonstrate three-photon quantum operation of an integrated device containing three coupled interferometers, eight spatial modes and many classical and nonclassical interferences. This represents a critical advance over previous complexities and the first on-chip nonclassical interference with more than two photonic inputs. We introduce a new scheme to verify quantum behaviour, using classically characterised device elements and hierarchies of photon correlation functions. We accurately predict the device's quantum behaviour and show operation inconsistent with both classical and bi-separable quantum models. Such methods for verifying multiphoton quantum behaviour are vital for achieving increased circuit complexity. Our experiment paves the way for the next generation of integrated photonic quantum simulation and computing devices., Comment: 7 pages, 4 figures