Long-distance continuous-variable quantum key distribution over 100-km fiber with local local oscillator.

Quantum key distribution (QKD) enables two remote parties to share encryption keys with security based on the laws of physics. Continuous-variable (CV) QKD with coherent states and coherent detection integrates well with existing telecommunication networks. Thus far, long-distance CV-QKD has only been demonstrated using a highly complex scheme where the local oscillator is transmitted, opening security loopholes for eavesdroppers and limiting potential applications. Here, we report a long-distance CV-QKD experiment with a locally generated local oscillator over a 100-kilometer fiber channel with a total loss of 15.4 decibels. This record-breaking distance is achieved by controlling the phase noise-induced excess noise through a machine learning framework for carrier recovery and optimizing the modulation variance. We implement the full CV-QKD protocol and demonstrate the generation of keys secure against collective attacks in the finite-size regime. Our results mark a substantial milestone for realizing CV quantum access networks with a high loss budget and pave the way for large-scale deployment of secure QKD.

Fully guided and phase locked Ti:PPLN waveguide squeezing for applications in quantum sensing.

This work reports a fully guided setup for single-mode squeezing on integrated titanium-indiffused periodically poled nonlinear resonators. A continuous-wave laser beam is delivered and the squeezed field is collected by single-mode fibers; up to -3.17(9) dB of useful squeezing is available in fibers. To showcase the usefulness of such a fiber-coupled device, we applied the generated squeezed light in a fiber-based phase sensing experiment, showing a quantum enhancement in the signal-to-noise ratio of 0.35 dB. Moreover, our investigation of the effect of photorefraction on the cavity resonance condition suggests that it causes system instabilities at high powers.

Deterministic Quantum Phase Estimation beyond N00N States.

The modern scientific method is critically dependent on precision measurements of physical parameters. A classic example is the measurement of the optical phase enabled by optical interferometry, where the error on the measured phase is conventionally bounded by the so-called Heisenberg limit. To achieve phase estimation at the Heisenberg limit, it has been common to consider protocols based on highly complex N00N states of light. However, despite decades of research and several experimental explorations, there has been no demonstration of deterministic phase estimation with N00N states reaching the Heisenberg limit or even surpassing the shot noise limit. Here we use a deterministic phase estimation scheme based on a source of Gaussian squeezed vacuum states and high-efficiency homodyne detection to obtain phase estimates with an extreme sensitivity that significantly surpasses the shot noise limit and even beats the conventional Heisenberg limit as well as the performance of a pure N00N state protocol. Using a high-efficiency setup with a total loss of about 11%, we achieve a Fisher information of 15.8(6) rad^{-2} per photon-a significant increase in performance compared to state of the art and beyond an ideal six photon N00N state scheme. This work represents an important achievement in quantum metrology, and it opens the door to future quantum sensing technologies for the interrogation of light-sensitive biological systems.

Charge Stability and Charge-State-Based Spin Readout of Shallow Nitrogen-Vacancy Centers in Diamond.

Spin-based applications of the negatively charged nitrogen-vacancy (NV) center in diamonds require an efficient spin readout. One approach is the spin-to-charge conversion (SCC), relying on mapping the spin states onto the neutral (NV0) and negative (NV-) charge states followed by a subsequent charge readout. With high charge-state stability, SCC enables extended measurement times, increasing precision and minimizing noise in the readout compared to the commonly used fluorescence detection. Nanoscale sensing applications, however, require shallow NV centers within a few nanometers distance from the surface where surface related effects might degrade the NV charge state. In this article, we investigate the charge state initialization and stability of single NV centers implanted ≈5 nm below the surface of a flat diamond plate. We demonstrate the SCC protocol on four shallow NV centers suitable for nanoscale sensing, obtaining a reduced readout noise of 5-6 times the spin-projection noise limit. We investigate the general applicability of the SCC for shallow NV centers and observe a correlation between the NV charge-state stability and readout noise. Coating the diamond with glycerol improves both the charge initialization and stability. Our results reveal the influence of the surface-related charge environment on the NV charge properties and motivate further investigations to functionalize the diamond surface with glycerol or other materials for charge-state stabilization and efficient spin-state readout of shallow NV centers suitable for nanoscale sensing.

Practical continuous-variable quantum key distribution with composable security.

A quantum key distribution (QKD) system must fulfill the requirement of universal composability to ensure that any cryptographic application (using the QKD system) is also secure. Furthermore, the theoretical proof responsible for security analysis and key generation should cater to the number N of the distributed quantum states being finite in practice. Continuous-variable (CV) QKD based on coherent states, despite being a suitable candidate for integration in the telecom infrastructure, has so far been unable to demonstrate composability as existing proofs require a rather large N for successful key generation. Here we report a Gaussian-modulated coherent state CVQKD system that is able to overcome these challenges and can generate composable keys secure against collective attacks with N ≈ 2 × 108 coherent states. With this advance, possible due to improvements to the security proof and a fast, yet low-noise and highly stable system operation, CVQKD implementations take a significant step towards their discrete-variable counterparts in practicality, performance, and security.

Protocol for Generating Optical Gottesman-Kitaev-Preskill States with Cavity QED.

Gottesman-Kitaev-Preskill (GKP) states are a central resource for fault-tolerant optical continuous-variable quantum computing. However, their realization in the optical domain remains to be demonstrated. Here we propose a method for preparing GKP states using a cavity QED system that can be realized in several platforms, such as trapped atoms, quantum dots, or diamond color centers. We then further combine the protocol with the previously proposed breeding protocol by Vasconcelos et al. to relax the demands on the quality of the QED system, finding that GKP states with more than 10 dB squeezing could be achieved in near-future experiments.

Homodyne-based quantum random number generator at 2.9 Gbps secure against quantum side-information.

Quantum random number generators promise perfectly unpredictable random numbers. A popular approach to quantum random number generation is homodyne measurements of the vacuum state, the ground state of the electro-magnetic field. Here we experimentally implement such a quantum random number generator, and derive a security proof that considers quantum side-information instead of classical side-information only. Based on the assumptions of Gaussianity and stationarity of noise processes, our security analysis furthermore includes correlations between consecutive measurement outcomes due to finite detection bandwidth, as well as analog-to-digital converter imperfections. We characterize our experimental realization by bounding measured parameters of the stochastic model determining the min-entropy of the system's measurement outcomes, and we demonstrate a real-time generation rate of 2.9 Gbit/s. Our generator follows a trusted, device-dependent, approach. By treating side-information quantum mechanically an important restriction on adversaries is removed, which usually was reserved to semi-device-independent and device-independent schemes.

Photophysics of quantum emitters in hexagonal boron-nitride nano-flakes.

Quantum emitters in hexagonal boron nitride (hBN) have attracted significant interest due to their bright and narrowband photon emission even at room temperature. The wide-bandgap two-dimensional material incorporates crystal defects of yet-unknown configuration, introducing discrete energy levels with radiative transition frequencies in the visible spectral range. The commonly observed high brightness together with the moderate fluorescence lifetime indicates a high quantum efficiency, but the exact dynamics and the underlying energy level structure remain elusive. In this study we present a systematic and detailed analysis of the photon statistics recorded for several individual emitters. We extract the individual decay rates by modeling the second-order correlation functions using a set of rate equations based on an energy level scheme involving long-lived states. Our analysis clearly indicates excitation-power-dependent non-radiative couplings to at least two metastable levels and confirms a near unity quantum efficiency.

Tomography of a Feedback Measurement with Photon Detection.

Quantum measurement is essential to both the foundations and practical applications of quantum information science. Among many possible models of quantum measurement, feedback measurements that dynamically update their physical structure are highly interesting due to their flexibility, which enables a wide range of measurements that might otherwise be hard to implement. Here we investigate by detector tomography a measurement consisting of a displacement operation combined with photon detection followed by a real time feedback operation. We design the measurement in order to discriminate the superposition of vacuum and single photon states-the single-rail qubit-and find that it can discriminate the superposition states with a certainty of 96%. Such a feedback-controlled photon counter will facilitate the realization of quantum information protocols with single-rail qubits as well as the nonlocality test of certain entangled states.

Deterministic generation of a two-dimensional cluster state.

Measurement-based quantum computation offers exponential computational speed-up through simple measurements on a large entangled cluster state. We propose and demonstrate a scalable scheme for the generation of photonic cluster states suitable for universal measurement-based quantum computation. We exploit temporal multiplexing of squeezed light modes, delay loops, and beam-splitter transformations to deterministically generate a cylindrical cluster state with a two-dimensional (2D) topological structure as required for universal quantum information processing. The generated state consists of more than 30,000 entangled modes arranged in a cylindrical lattice with 24 modes on the circumference, defining the input register, and a length of 1250 modes, defining the computation depth. Our demonstrated source of two-dimensional cluster states can be combined with quantum error correction to enable fault-tolerant quantum computation.

Clock transition by continuous dynamical decoupling of a three-level system.

We present a novel continuous dynamical decoupling scheme for the construction of a robust qubit in a three-level system. By means of a clock transition adjustment, we first show how robustness to environmental noise is achieved, while eliminating drive-noise, to first-order. We demonstrate this scheme with the spin sub-levels of the NV-centre's electronic ground state. By applying drive fields with moderate Rabi frequencies, the drive noise is eliminated and an improvement of 2 orders of magnitude in the coherence time is obtained compared to the pure dephasing time. We then show how the clock transition adjustment can be tuned to eliminate also the second-order effect of the environmental noise with moderate drive fields. A further detailed theoretical investigation suggests an additional improvement of more than 1 order of magnitude in the coherence time which is supported by simulations. Hence, our scheme predicts that the coherence time may be prolonged towards the lifetime-limit using a relatively simple experimental setup.

Contributed Review: Camera-limits for wide-field magnetic resonance imaging with a nitrogen-vacancy spin sensor.

Sensitive, real-time optical magnetometry with nitrogen-vacancy centers in diamond relies on accurate imaging of small (≪10-2), fractional fluorescence changes across the diamond sample. We discuss the limitations on magnetic field sensitivity resulting from the limited number of photoelectrons that a camera can record in a given time. Several types of camera sensors are analyzed, and the smallest measurable magnetic field change is estimated for each type. We show that most common sensors are of a limited use in such applications, while certain highly specific cameras allow achieving nanotesla-level sensitivity in 1 s of a combined exposure. Finally, we demonstrate the results obtained with a lock-in camera that paves the way for real-time, wide-field magnetometry at the nanotesla level and with a micrometer resolution.

Narrow-bandwidth sensing of high-frequency fields with continuous dynamical decoupling.

State-of-the-art methods for sensing weak AC fields are only efficient in the low frequency domain (<10 MHz). The inefficiency of sensing high-frequency signals is due to the lack of ability to use dynamical decoupling. In this paper we show that dynamical decoupling can be incorporated into high-frequency sensing schemes and by this we demonstrate that the high sensitivity achieved for low frequency can be extended to the whole spectrum. While our scheme is general and suitable to a variety of atomic and solid-state systems, we experimentally demonstrate it with the nitrogen-vacancy center in diamond. For a diamond with natural abundance of 13C, we achieve coherence times up to 1.43 ms resulting in a smallest detectable magnetic field strength of 4 nT at 1.6 GHz. Attributed to the inherent nature of our scheme, we observe an additional increase in coherence time due to the signal itself.

Optimised frequency modulation for continuous-wave optical magnetic resonance sensing using nitrogen-vacancy ensembles.

Magnetometers based on ensembles of nitrogen-vacancy centres are a promising platform for continuously sensing static and low-frequency magnetic fields. Their combination with phase-sensitive (lock-in) detection creates a highly versatile sensor with a sensitivity that is proportional to the derivative of the optical magnetic resonance lock-in spectrum, which is in turn dependant on the lock-in modulation parameters. Here we study the dependence of the lock-in spectral slope on the modulation of the spin-driving microwave field. Given the presence of the intrinsic nitrogen hyperfine spin transitions, we experimentally show that when the ratio between the hyperfine linewidth and their separation is ≳ 1/4, square-wave based frequency modulation generates the steepest slope at modulation depths exceeding the separation of the hyperfine lines, compared to sine-wave based modulation. We formulate a model for calculating lock-in spectra which shows excellent agreement with our experiments, and which shows that an optimum slope is achieved when the linewidth/separation ratio is ≲ 1/4 and the modulation depth is less then the resonance linewidth, irrespective of the modulation function used.

Continuous-variable quantum computing on encrypted data.

The ability to perform computations on encrypted data is a powerful tool for protecting a client's privacy, especially in today's era of cloud and distributed computing. In terms of privacy, the best solutions that classical techniques can achieve are unfortunately not unconditionally secure in the sense that they are dependent on a hacker's computational power. Here we theoretically investigate, and experimentally demonstrate with Gaussian displacement and squeezing operations, a quantum solution that achieves the security of a user's privacy using the practical technology of continuous variables. We demonstrate losses of up to 10 km both ways between the client and the server and show that security can still be achieved. Our approach offers a number of practical benefits (from a quantum perspective) that could one day allow the potential widespread adoption of this quantum technology in future cloud-based computing networks.

Determining the internal quantum efficiency of shallow-implanted nitrogen-vacancy defects in bulk diamond.

It is generally accepted that nitrogen-vacancy (NV) defects in bulk diamond are bright sources of luminescence. However, the exact value of their internal quantum efficiency (IQE) has not been measured so far. Here we use an implementation of Drexhage's scheme to quantify the IQE of shallow-implanted NV defects in a single-crystal bulk diamond. Using a spherical metallic mirror with a large radius of curvature compared to the optical spot size, we perform calibrated modifications of the local density of states around NV defects and observe the change of their total decay rate, which is further used for IQE quantification. We also show that at the excitation wavelength of 532 nm, photo-induced relaxation cannot be neglected even at moderate excitation powers well below the saturation level. For NV defects shallow implanted 4.5 ± 1 and 8 ± 2 nm below the diamond surface, we determine the quantum efficiency to be 0.70 ± 0.07 and 0.82 ± 0.08, respectively.

Quantum enhanced feedback cooling of a mechanical oscillator using nonclassical light.

Laser cooling is a fundamental technique used in primary atomic frequency standards, quantum computers, quantum condensed matter physics and tests of fundamental physics, among other areas. It has been known since the early 1990s that laser cooling can, in principle, be improved by using squeezed light as an electromagnetic reservoir; while quantum feedback control using a squeezed light probe is also predicted to allow improved cooling. Here we show the implementation of quantum feedback control of a micro-mechanical oscillator using squeezed probe light. This allows quantum-enhanced feedback cooling with a measurement rate greater than it is possible with classical light, and a consequent reduction in the final oscillator temperature. Our results have significance for future applications in areas ranging from quantum information networks, to quantum-enhanced force and displacement measurements and fundamental tests of macroscopic quantum mechanics.

Measurement-Induced Macroscopic Superposition States in Cavity Optomechanics.

A novel protocol for generating quantum superpositions of macroscopically distinct states of a bulk mechanical oscillator is proposed, compatible with existing optomechanical devices operating in the bad-cavity limit. By combining a pulsed optomechanical quantum nondemolition (QND) interaction with nonclassical optical resources and measurement-induced feedback, the need for strong single-photon coupling is avoided. We outline a three-pulse sequence of QND interactions encompassing squeezing-enhanced cooling by measurement, state preparation, and tomography.