Entangling remote qubits using the single-photon protocol: an in-depth theoretical and experimental study
Sophie Hermans, Matteo Pompili, Laura dos Santos Martins, Alejandro R.‐P. Montblanch, Hans K. C. Beukers, Simon Baier, Johannes Borregaard, Ronald Hanson
Abstract The generation of entanglement between remote matter qubits has developed into a key capability for fundamental investigations as well as for emerging quantum technologies. In the single-photon, protocol entanglement is heralded by generation of qubit-photon entangled states and subsequent detection of a single photon behind a beam splitter. In this work we perform a detailed theoretical and experimental investigation of this protocol and its various sources of infidelity. We develop an extensive theoretical model and subsequently tailor it to our experimental setting, based on nitrogen-vacancy centers in diamond. Experimentally, we verify the model by generating remote states for varying phase and amplitudes of the initial qubit superposition states and varying optical phase difference of the photons arriving at the beam splitter. We show that a static frequency offset between the optical transitions of the qubits leads to an entangled state phase that depends on the photon detection time. We find that the implementation of a Charge-Resonance check on the nitrogen-vacancy center yields transform-limited linewidths. Moreover, we measure the probability of double optical excitation, a significant source of infidelity, as a function of the power of the excitation pulse. Finally, we find that imperfect optical excitation can lead to a detection-arm-dependent entangled state fidelity and rate. The conclusion presented here are not specific to the nitrogen-vacancy centers used to carry out the experiments, and are therefore readily applicable to other qubit platforms.
Abstract The generation of entanglement between remote matter qubits has developed into a key capability for fundamental investigations as well as for emerging quantum technologies. In the single-photon, protocol entanglement is heralded by generation of qubit-photon entangled states and subsequent detection of a single photon behind a beam splitter. In this work we perform a detailed theoretical and experimental investigation of this protocol and its various sources of infidelity. We develop an extensive theoretical model and subsequently tailor it to our experimental setting, based on nitrogen-vacancy centers in diamond. Experimentally, we verify the model by generating remote states for varying phase and amplitudes of the initial qubit superposition states and varying optical phase difference of the photons arriving at the beam splitter. We show that a static frequency offset between the optical transitions of the qubits leads to an entangled state phase that depends on the photon detection time. We find that the implementation of a Charge-Resonance check on the nitrogen-vacancy center yields transform-limited linewidths. Moreover, we measure the probability of double optical excitation, a significant source of infidelity, as a function of the power of the excitation pulse. Finally, we find that imperfect optical excitation can lead to a detection-arm-dependent entangled state fidelity and rate. The conclusion presented here are not specific to the nitrogen-vacancy centers used to carry out the experiments, and are therefore readily applicable to other qubit platforms.
A general entanglement generation protocol between remote stationary qubits using single-photon reflection in a photonic network is explored theoretically. The nodes of the network consist of single qubits that are typically represented by the spin of a color center, each localized in a separate optical cavity and linked to other nodes via photonic links such as optical fibers. We derive a model applicable to a wide range of parameters and scenarios to describe the nodes and the local spin-photon interaction accounting for the pulsed (finite-bandwidth) nature of flying single photons while optimizing the rate and fidelity. We investigate entanglement generation between remote qubits and tailor protocols to a variety of physical implementations with different properties. Of particular interest is the regime of weak coupling and low cooperativity between the spin and cavity, which is relevant in the cases of the nitrogen- and silicon-vacancy centers in diamond. We also take into account the variability of the properties between realistic (stationary) nodes.
Path entanglement is an essential resource for photonic quantum information processing, including in quantum computing, quantum communication, and quantum sensing. In this work, we experimentally study the generation and verification of bipartite path-entangled states using single photons produced by a nitrogen vacancy center within a nanodiamond. We perform a range of measurements to characterize the photons being generated and verify the presence of path entanglement. The experiment is performed using continuous-wave laser excitation and a novel, to our knowledge, state-generation 'time-window' method. This approach to path entanglement verification is different from previous work as it does not make use of a pulsed laser excitation source.
In this thesis we experimentally investigate quantum nonlocality: entangled states of spatially separated objects. Entanglement is one of the most striking consequences of the quantum formalism developed in the 1920's; the predicted outcomes of independent measurements on entangled objects reveal strong correlations that cannot be explained by classical physics. Early on, such predictions led physicists to doubt the validity and completeness of quantum theory. At the same time, entanglement is a key resource for applications in quantum information processing and a pre-requisite for many tasks in quantum communication and computation. This thesis attempts to answer two application driven questions: Firstly, can we generate useful entangled states of solid state spins for applications in quantum information processing? Secondly, can we use such entangled states as a resource to teleport an unknown quantum state? Finally, we ask a foundational question: Are our entangled states indeed inconsistent with the classical notions of free choice, locality and realism? Can we prove this experimentally, under the minimal assumptions of a loophole-free Bell test? To answer these questions we use single spins in ultra-pure diamonds. In particular, we use the electronic and nuclear spins associated with single nitrogen-vacancy (NV) defects. The NV centre is a point defect in diamond, consisting of a substitutional nitrogen (N) atom and a neighbouring missing carbon atom (vacancy, V). The NV centre possesses bound electronic states, whose energy levels lie well within the bandgap of the diamond host and whose spin degree of freedom can be used as a quantum bit (qubit). Because of the large diamond bandgap and the 99% spin free carbon-12 environment, the electronic spin qubit has exceptional coherence properties even at room temperature. Optical and microwave fields allow control of the electronic spin, which in turn allows control of nearby nuclear spins (the host nitrogen nuclear spin, and nearby carbon-13 spins). At liquid helium temperatures, spin-preserving optical transitions provide a powerful optical interface to the electronic spin, allowing, for example, projective readout of the spin state. By employing a protocol where entanglement is heralded by the detection of a single photon from each of two NV centres in diamonds separated by three metres, we find we can answer the first question in the affirmative. We show for the first time heralded entanglement between solid state quantum systems separated by a human-scale distance. Then, by combining the heralded entanglement with a deterministic local Bell state measurement and fast feed-forward, we show for the first time unconditional quantum teleportation over human-scale distances. We teleport an unknown quantum state from a nuclear spin in one diamond to an electronic spin in a diamond three meters away. Finally, by employing techniques from the previous experiments, we implement the first loophole-free Bell test. We separate two diamonds by 1.3 kilometres and optimize all operational fidelities, collection efficiencies and rates. This allows us to generate heralded entanglement between them approximately once an hour. The distance provides us with time to read out the electronic spin state in each diamond, faster than any lightlike signal could travel between them. The high-fidelity entangled state preparation and spin readout are sufficient to violate the Clauser-Horne-Shimony-Holt Bell-inequality. Combined with fast random number generators and a robust statistical analysis, we find a significant rejection of the local-realist hypothesis, without requiring additional experimental assumptions. The results in this thesis open the door to various applications in quantum information processing. In particular, a remote photonic entangling operation may enable future quantum networks. In such a network the nodes would be formed by the NV centre's combined electronic and nuclear spin register. The nodes would be linked by photonic entanglement operations. Such a network could be used for long distance secure communication, provide a connection between separated quantum computers, or form the basis of a fault tolerant quantum computer by itself. Furthermore, a loophole-free Bell test demonstrates the possibility to do device independent randomness generation and key distribution, that could form the basis for future secure communication channels.
Quantum entanglement, a key resource for quantum information science, is inherent in a solid. It has been recently shown that entanglement between a single optical photon and a single spin qubit in a solid is generated via spontaneous emission. However, entanglement generation by measurement is rather essential for quantum operations. We here show that the physics behind the entangled emission can be time reversed to demonstrate entangled absorption mediated by an inherent spin-orbit entanglement in a single nitrogen vacancy center in diamond. Optical arbitrary spin state preparation and complete spin state tomography reveal the fidelity of the entangled absorption to be 95%. With the entangled emission and absorption of a photon, materials can be spontaneously entangled or swap their quantum state based on the quantum teleportation scheme.
We propose efficient schemes of direct concurrence measurement for two-qubit spin and photon-polarization entangled states via the interaction between single-photon pulses and nitrogen-vacancy (NV) centers in diamond embedded in optical microcavities. For different entangled-state types, diversified quantum devices and operations are designed accordingly. The initial unknown entangled states are possessed by two spatially separated participants, and nonlocal spin (polarization) entanglement can be measured with the aid of detection probabilities of photon (NV center) states. This non-demolition entanglement measurement manner makes initial entangled particle-pair avoid complete annihilation but evolve into corresponding maximally entangled states. Moreover, joint inter-qubit operation or global qubit readout is not required for the presented schemes and the final analyses inform favorable performance under the current parameters conditions in laboratory. The unique advantages of spin qubits assure our schemes wide potential applications in spin-based solid quantum information and computation.
Diamond tin-vacancy centers have emerged as a promising platform for quantum information science and technology. A key challenge for their use in more-complex quantum experiments and scalable applications is the ability to prepare the center in the desired charge state with the optical transition at a predefined frequency. Here we report on heralding such successful preparation using a combination of laser excitation, photon detection, and real-time logic. We first show that fluorescence photon counts collected during an optimized resonant probe pulse strongly correlate with the subsequent charge state and optical-transition frequency, enabling real-time heralding of the desired state through threshold photon counting. We then implement and apply this heralding technique to photoluminescence-excitation measurements, coherent optical driving, and an optical Ramsey experiment, finding strongly increased optical coherence with increasing threshold. Finally, we demonstrate that the prepared optical frequency follows the probe laser across the inhomogeneous linewidth, enabling tuning of the transition frequency over multiple homogeneous linewidths. Published by the American Physical Society 2024