Multistage entanglement swapping

Multistage entanglement swapping using superconducting qubits in the absence and presence of dissipative environment without Bell state measurement

In recent decades the entangled state generation is of great importance in the quantum information processing and technologies. In this paper, producing the distributed entangled state of superconducting (SC) qubits is considered using an entanglement swapping protocol in three successive stages. The SC qubit pairs [Formula: see text] with [Formula: see text], where each pair of the qubits has been placed on a separate chip, are initially prepared in maximally entangled states. The external magnetic fields on capacitively coupled pairs [Formula: see text] and [Formula: see text] are implemented for modulating the frequency of qubits. Then, the SC qubits [Formula: see text] and [Formula: see text] are converted into entangled states via operating proper measurements instead of Bell state measurement (which is generally a hard task). Finally, the distributed entangled state of target SC qubits [Formula: see text] can be obtained by applying external magnetic fields on qubits [Formula: see text] and via operating suitable measurements. This process is studied in the absence and presence of thermal decoherence effects. The concurrence, as a measure of entanglement between two target qubits, success probability of the distributed entangled states and the corresponding fidelities are evaluated, by which we find that the state of target SC qubits [Formula: see text] is converted to Bell state with maximum entanglement at some moments of time. Under appropriate conditions the maximum of success probability of the obtained states in each stage approaches 1. However, the maxima of concurrence and success probability gradually decrease due to the thermal noise as time goes on. Moreover, compelling amounts of fidelity, success probability and entanglement can be obtained for the achieved entangled states.

Complete Frequency-Bin Bell Basis Synthesizer

We report the experimental generation of all four frequency-bin Bell states in a single versatile setup via successive pumping of spontaneous parametric down-conversion with single and dual spectral lines. Our scheme utilizes intensity modulation to control the pump configuration and offers turn-key generation of any desired Bell state using only off-the-shelf telecommunication equipment. We employ Bayesian inference to reconstruct the density matrices of the generated Bell states, finding fidelities ≥97% for all cases. Additionally, we demonstrate the sensitivity of the frequency-bin Bell states to common-mode and differential-mode temporal delays traversed by the photons comprising the state-presenting the potential for either enhanced resolution or nonlocal sensing enabled by our complete Bell basis synthesizer.

Quantum Correlation Swapping between Two Werner States Undergoing Local and Nonlocal Unitary Operations

In this paper, quantum correlation (QC) swapping between two Werner-like states, which are transformed from Werner states undergoing local and nonlocal unitary operations, are studied. Bell states measures are performed in the middle node to realize the QC swapping and correspondingly final correlated sates are obtained. Two different QC quantifiers, i.e., measurement-induced disturbance (MID) and ameliorated MID, are employed to characterize and quantify all the concerned QCs in the swapping process. All QCs in the concerned states are evaluated analytically and numerically. Correspondingly, their characteristics and properties are exposed in detail. It is exposed that, through the QC swapping process, one can obtain the long-distance QC indeed. Moreover, the similarities of monotony features of MID and AMID between the initial states and final states are exposed and analyzed.

Reducing circuit complexity in optical quantum computation using 3D architectures

Integrated photonic architectures based on optical waveguides are one of the leading candidates for the future realisation of large-scale quantum computation. One of the central challenges in realising this goal is simultaneously minimising loss whilst maximising interferometric visibility within waveguide circuits. One approach is to reduce circuit complexity and depth. A major constraint in most planar waveguide systems is that beamsplitter transformations between distant optical modes require numerous intermediate SWAP operations to couple them into nearest neighbour proximity, each of which introduces loss and scattering. Here, we propose a 3D architecture which can significantly mitigate this problem by geometrically bypassing trivial intermediate operations. We demonstrate the viability of this concept by considering a worst-case 2D scenario, where we interfere the two most distant optical modes in a planar structure. Using femtosecond laser direct-writing technology we experimentally construct a 2D architecture to implement Hong-Ou-Mandel interference between its most distant modes, and a 3D one with corresponding physical dimensions, demonstrating significant improvement in both fidelity and efficiency in the latter case. In addition to improving fidelity and efficiency of individual non-adjacent beamsplitter operations, this approach provides an avenue for reducing the optical depth of circuits comprising complex arrays of beamsplitter operations.

Bell nonlocality in networks

Bell's theorem proves that quantum theory is inconsistent with local physical models. It has propelled research in the foundations of quantum theory and quantum information science. As a fundamental feature of quantum theory, it impacts predictions far beyond the traditional scenario of the Einstein-Podolsky-Rosen paradox. In the last decade, the investigation of nonlocality has moved beyond Bell's theorem to consider more sophisticated experiments that involve several independent sources which distribute shares of physical systems among many parties in a network. Network scenarios, and the nonlocal correlations that they give rise to, lead to phenomena that have no counterpart in traditional Bell experiments, thus presenting a formidable conceptual and practical challenge. This review discusses the main concepts, methods, results and future challenges in the emerging topic of Bell nonlocality in networks.

Increasing Quantum Correlations Based on Measurement-Induced Disturbance via a Swapping Procedure with Two-Qubit Mixed States

In this paper, quantum correlation (QC) swapping for certain separable two-qubit mixed states is treated. A QC quantifier, measurement-induced disturbance (MID) (Luo in Phys Rev A 77:022301, 2008), is employed to characterize and quantify QCs in the relevant states. Properties of all QCs in the swapping process are revealed. Particularly, it is found that MID can be increased through QC swapping for certain separable two-qubit mixed states.

Scalable distributed gate-model quantum computers

A scalable model for a distributed quantum computation is a challenging problem due to the complexity of the problem space provided by the diversity of possible quantum systems, from small-scale quantum devices to large-scale quantum computers. Here, we define a model of scalable distributed gate-model quantum computation in near-term quantum systems of the NISQ (noisy intermediate scale quantum) technology era. We prove that the proposed architecture can maximize an objective function of a computational problem in a distributed manner. We study the impacts of decoherence on distributed objective function evaluation.

Resource prioritization and balancing for the quantum internet

The quantum Internet enables networking based on the fundamentals of quantum mechanics. Here, methods and procedures of resource prioritization and resource balancing are defined for the quantum Internet. We define a model for resource consumption optimization in quantum repeaters, and a strongly-entangled network structure for resource balancing. We study the resource-balancing efficiency of the strongly-entangled structure. We prove that a strongly-entangled quantum network is two times more efficient in a resource balancing problem than a full-mesh network of the traditional Internet.

Dynamics of entangled networks of the quantum Internet

Entangled quantum networks are a fundamental of any global-scale quantum Internet. Here, a mathematical model is developed to quantify the dynamics of entangled network structures and entanglement flow in the quantum Internet. The analytical solutions of the model determine the equilibrium states of the entangled quantum networks and characterize the stability, fluctuation attributes, and dynamics of entanglement flow in entangled network structures. We demonstrate the results of the model through various entangled structures and quantify the dynamics.

Routing space exploration for scalable routing in the quantum Internet

The entangled network structure of the quantum Internet formulates a high complexity routing space that is hard to explore. Scalable routing is a routing method that can determine an optimal routing at particular subnetwork conditions in the quantum Internet to perform a high-performance and low-complexity routing in the entangled structure. Here, we define a method for routing space exploration and scalable routing in the quantum Internet. We prove that scalable routing allows a compact and efficient routing in the entangled networks of the quantum Internet.

Theory of Noise-Scaled Stability Bounds and Entanglement Rate Maximization in the Quantum Internet

Crucial problems of the quantum Internet are the derivation of stability properties of quantum repeaters and theory of entanglement rate maximization in an entangled network structure. The stability property of a quantum repeater entails that all incoming density matrices can be swapped with a target density matrix. The strong stability of a quantum repeater implies stable entanglement swapping with the boundness of stored density matrices in the quantum memory and the boundness of delays. Here, a theoretical framework of noise-scaled stability analysis and entanglement rate maximization is conceived for the quantum Internet. We define the term of entanglement swapping set that models the status of quantum memory of a quantum repeater with the stored density matrices. We determine the optimal entanglement swapping method that maximizes the entanglement rate of the quantum repeaters at the different entanglement swapping sets as function of the noise of the local memory and local operations. We prove the stability properties for non-complete entanglement swapping sets, complete entanglement swapping sets and perfect entanglement swapping sets. We prove the entanglement rates for the different entanglement swapping sets and noise levels. The results can be applied to the experimental quantum Internet.

Optimizing High-Efficiency Quantum Memory with Quantum Machine Learning for Near-Term Quantum Devices

Quantum memories are a fundamental of any global-scale quantum Internet, high-performance quantum networking and near-term quantum computers. A main problem of quantum memories is the low retrieval efficiency of the quantum systems from the quantum registers of the quantum memory. Here, we define a novel quantum memory called high-retrieval-efficiency (HRE) quantum memory for near-term quantum devices. An HRE quantum memory unit integrates local unitary operations on its hardware level for the optimization of the readout procedure and utilizes the advanced techniques of quantum machine learning. We define the integrated unitary operations of an HRE quantum memory, prove the learning procedure, and evaluate the achievable output signal-to-noise ratio values. We prove that the local unitaries of an HRE quantum memory achieve the optimization of the readout procedure in an unsupervised manner without the use of any labeled data or training sequences. We show that the readout procedure of an HRE quantum memory is realized in a completely blind manner without any information about the input quantum system or about the unknown quantum operation of the quantum register. We evaluate the retrieval efficiency of an HRE quantum memory and the output SNR (signal-to-noise ratio). The results are particularly convenient for gate-model quantum computers and the near-term quantum devices of the quantum Internet.

Opportunistic Entanglement Distribution for the Quantum Internet

Quantum entanglement is a building block of the entangled quantum networks of the quantum Internet. A fundamental problem of the quantum Internet is entanglement distribution. Since quantum entanglement will be fundamental to any future quantum networking scenarios, the distribution mechanism of quantum entanglement is a critical and emerging issue in quantum networks. Here we define the method of opportunistic entanglement distribution for the quantum Internet. The opportunistic model defines distribution sets that are aimed to select those quantum nodes for which the cost function picks up a local minimum. The cost function utilizes the error patterns of the local quantum memories and the predictability of the evolution of the entanglement fidelities. Our method provides efficient entanglement distributing with respect to the actual statuses of the local quantum memories of the node pairs. The model provides an easily-applicable, moderate-complexity solution for high-fidelity entanglement distribution in experimental quantum Internet scenarios.

Counterfactual entanglement swapping enables high-efficiency entanglement distribution

We propose an alternative entanglement swapping scheme based on the principle of the counterfactual quantum communication, which demonstrates nonlocal entanglement swapping can be achieved by the operations of a third party. During the whole process, it is not needed to transmit any physical particles among the participants. Furthermore, all the entangled particles are not destroyed in the counterfactual entanglement swapping process, which means we can obtain two pairs of nonlocal entanglement at the same time, thus achieve high-efficiency entanglement distribution. The numerical analysis about the performance of the presented scheme shows that this counterfactual protocol can be implemented with high success probability and fidelity in the ideal asymptotic limit. The scheme may be meaningful for large-scale quantum communication network and quantum repeater.

Entanglement Availability Differentiation Service for the Quantum Internet

A fundamental concept of the quantum Internet is quantum entanglement. In a quantum Internet scenario where the legal users of the network have different priority levels or where a differentiation of entanglement availability between the users is a necessity, an entanglement availability service is essential. Here we define the entanglement availability differentiation (EAD) service for the quantum Internet. In the proposed EAD framework, the differentiation is either made in the amount of entanglement with respect to the relative entropy of entanglement associated with the legal users, or in the time domain with respect to the amount of time that is required to establish a maximally entangled system between the legal parties. The framework provides an efficient and easily-implementable solution for the differentiation of entanglement availability in experimental quantum networking scenarios.

Two-Hierarchy Entanglement Swapping for a Linear Optical Quantum Repeater

Quantum repeaters play a significant role in achieving long-distance quantum communication. In the past decades, tremendous effort has been devoted towards constructing a quantum repeater. As one of the crucial elements, entanglement has been created in different memory systems via entanglement swapping. The realization of j-hierarchy entanglement swapping, i.e., connecting quantum memory and further extending the communication distance, is important for implementing a practical quantum repeater. Here, we report the first demonstration of a fault-tolerant two-hierarchy entanglement swapping with linear optics using parametric down-conversion sources. In the experiment, the dominant or most probable noise terms in the one-hierarchy entanglement swapping, which is on the same order of magnitude as the desired state and prevents further entanglement connections, are automatically washed out by a proper design of the detection setting, and the communication distance can be extended. Given suitable quantum memory, our techniques can be directly applied to implementing an atomic ensemble based quantum repeater, and are of significant importance in the scalable quantum information processing.

Entanglement-Gradient Routing for Quantum Networks

We define the entanglement-gradient routing scheme for quantum repeater networks. The routing framework fuses the fundamentals of swarm intelligence and quantum Shannon theory. Swarm intelligence provides nature-inspired solutions for problem solving. Motivated by models of social insect behavior, the routing is performed using parallel threads to determine the shortest path via the entanglement gradient coefficient, which describes the feasibility of the entangled links and paths of the network. The routing metrics are derived from the characteristics of entanglement transmission and relevant measures of entanglement distribution in quantum networks. The method allows a moderate complexity decentralized routing in quantum repeater networks. The results can be applied in experimental quantum networking, future quantum Internet, and long-distance quantum communications.

Experimental Demonstration of a Hybrid-Quantum-Emitter Producing Individual Entangled Photon Pairs in the Telecom Band

Quantum emitters generating individual entangled photon pairs (IEPP) have significant fundamental advantages over schemes that suffer from multiple photon emission, or schemes that require post-selection techniques or the use of photon-number discriminating detectors. Quantum dots embedded within nanowires (QD-NWs) represent one of the most promising candidate for quantum emitters that provide a high collection efficiency of photons. However, a quantum emitter that generates IEPP in the telecom band is still an issue demanding a prompt solution. Here, we demonstrate in principle that IEPPs in the telecom band can be created by combining a single QD-NW and a nonlinear crystal waveguide. The QD-NW system serves as the single photon source, and the emitted visible single photons are split into IEPPs at approximately 1.55 μm through the process of spontaneous parametric down conversion (SPDC) in a periodically poled lithium niobate (PPLN) waveguide. The compatibility of the QD-PPLN interface is the determinant factor in constructing this novel hybrid-quantum-emitter (HQE). Benefiting from the desirable optical properties of QD-NWs and the extremely high nonlinear conversion efficiency of PPLN waveguides, we successfully generate IEPPs in the telecom band with the polarization degree of freedom. The entanglement of the generated photon pairs is confirmed by the entanglement witness. Our experiment paves the way to producing HQEs inheriting the advantages of multiple systems.

Entanglement swapping between photons that have never coexisted

The role of the timing and order of quantum measurements is not just a fundamental question of quantum mechanics, but also a puzzling one. Any part of a quantum system that has finished evolving can be measured immediately or saved for later, without affecting the final results, regardless of the continued evolution of the rest of the system. In addition, the nonlocality of quantum mechanics, as manifested by entanglement, does not apply only to particles with spacelike separation, but also to particles with timelike separation. In order to demonstrate these principles, we generated and fully characterized an entangled pair of photons that have never coexisted. Using entanglement swapping between two temporally separated photon pairs, we entangle one photon from the first pair with another photon from the second pair. The first photon was detected even before the other was created. The observed two-photon state demonstrates that entanglement can be shared between timelike separated quantum systems.

Experimental activation of bound entanglement

Entanglement is one of the essential resources in quantum information and communication technology (QICT). The entanglement thus far explored and applied to QICT has been pure and distillable entanglement. Yet, there is another type of entanglement, called "bound entanglement," which is not distillable by local operations and classical communication. We demonstrate the experimental "activation" of the bound entanglement held in the four-qubit Smolin state, unleashing its immanent entanglement in distillable form, with the help of auxiliary two-qubit entanglement and local operations and classical communication. We anticipate that it opens the way to a new class of QICT applications that utilize more general classes of entanglement than ever, including bound entanglement.

Teleportation-based realization of an optical quantum two-qubit entangling gate

In recent years, there has been heightened interest in quantum teleportation, which allows for the transfer of unknown quantum states over arbitrary distances. Quantum teleportation not only serves as an essential ingredient in long-distance quantum communication, but also provides enabling technologies for practical quantum computation. Of particular interest is the scheme proposed by D. Gottesman and I. L. Chuang [(1999) Nature 402:390-393], showing that quantum gates can be implemented by teleporting qubits with the help of some special entangled states. Therefore, the construction of a quantum computer can be simply based on some multiparticle entangled states, Bell-state measurements, and single-qubit operations. The feasibility of this scheme relaxes experimental constraints on realizing universal quantum computation. Using two different methods, we demonstrate the smallest nontrivial module in such a scheme--a teleportation-based quantum entangling gate for two different photonic qubits. One uses a high-fidelity six-photon interferometer to realize controlled-NOT gates, and the other uses four-photon hyperentanglement to realize controlled-Phase gates. The results clearly demonstrate the working principles and the entangling capability of the gates. Our experiment represents an important step toward the realization of practical quantum computers and could lead to many further applications in linear optics quantum information processing.

Experimental multiparticle entanglement swapping for quantum networking

This Letter reports the first experimental demonstration of Greenberger-Horne-Zeilinger (GHZ) entanglement swapping. We start with three pairs of entangled photons. Upon projection of three single photons, each from an entangled pair, into a GHZ state, the other three originally independent photons are entangled in a GHZ state-creation of multiparticle entanglement without any direct interaction. This scheme may facilitate networks for quantum telephone exchange, multiparty quantum communication and distributed quantum computation.