"Event-ready-detectors" Bell experiment via entanglement swapping

Identifying Sources of Entanglement Loss in Photodriven Molecular Electron Spin Teleportation

We report on an electron donor-electron acceptor-stable radical (D-A-R•) molecule in which an electron spin state first prepared on R• is followed by photogeneration of an entangled singlet 1[D•+-A•-] spin pair to produce D•+-A•--R•. Since the A•- and R• spins within D•+-A•--R• are uncorrelated, spin teleportation from R• to D•+ occurs with a maximal 25% efficiency only for the singlet pair 1(A•--R•) by spin-allowed electron transfer from A•- to R•. However, since 1[D•+-A•-] is sufficiently long-lived, coherent spin mixing involving the unreactive 3(A•--R•) population affects entanglement and teleportation within D•+-A•--R•. Pulse electron paramagnetic resonance experiments show a direct correlation between electron spin flip-flops and entanglement loss, providing information for designing molecular materials to serve as nanoscale quantum device interconnects.

Quantum Nonlocality: Multicopy Resource Interconvertibility and Their Asymptotic Inequivalence

Quantum nonlocality, pioneered in Bell's seminal work and subsequently verified through a series of experiments, has drawn substantial attention due to its practical applications in various protocols. Evaluating and comparing the extent of nonlocality within distinct quantum correlations holds significant practical relevance. Within the resource theoretic framework this can be achieved by assessing the interconversion rate among different nonlocal correlations under free local operations and shared randomness. In this study we, however, present instances of quantum nonlocal correlations that are incomparable in the strongest sense. Specifically, when starting with an arbitrary many copies of one nonlocal correlation, it becomes impossible to obtain even a single copy of the other correlation, and this incomparability holds in both directions. Such incomparable quantum correlations can be obtained even in the simplest Bell scenario, which involves two parties, each having two dichotomic measurements setups. Notably, there exist an uncountable number of such incomparable correlations. Our result challenges the notion of a "unique gold coin," often referred to as the "maximally resourceful state," within the framework of the resource theory of quantum nonlocality. To this end, we provide examples of isotropic quantum correlations that cannot be distilled up to the Tsirelson point, and thus partially answer a long-standing open question in nonlocality distillation.

Symbolic model checking quantum circuits in Maude

This article presents a symbolic approach to model checking quantum circuits using a set of laws from quantum mechanics and basic matrix operations with Dirac notation. We use Maude, a high-level specification/programming language based on rewriting logic, to implement our symbolic approach. As case studies, we use the approach to formally specify several quantum communication protocols in the early work of quantum communication and formally verify their correctness: Superdense Coding, Quantum Teleportation, Quantum Secret Sharing, Entanglement Swapping, Quantum Gate Teleportation, Two Mirror-image Teleportation, and Quantum Network Coding. We demonstrate that our approach/implementation can be a first step toward a general framework to formally specify and verify quantum circuits in Maude. The proposed way to formally specify a quantum circuit makes it possible to describe the quantum circuit in Maude such that the formal specification can be regarded as a series of quantum gate/measurement applications. Once a quantum circuit has been formally specified in the proposed way together with an initial state and a desired property expressed in linear temporal logic (LTL), the proposed model checking technique utilizes a built-in Maude LTL model checker to automatically conduct formal verification that the quantum circuit enjoys the property starting from the initial state.

Optimal and scalable entanglement distribution over crossbar quantum networks

Crossbar networks are a cornerstone of network architectures, capable of operating both as standalone interconnections or as integral switching components in complex, multi-stage systems. The main advantages of crossbar networks are their non-blocking operation and unparalleled minimal latency. With the advent of large scale quantum networks, crossbars might be an important asset towards the Quantum Internet. This study proposes a solution for the problem of distributing entanglement within crossbar quantum networks. Entangled particles are a consumable resource in quantum networks, and are being used by most quantum protocols. By ensuring that nodes within quantum networks are being supplied with entanglement, the reliability and efficiency of the network is maintained. By providing an efficient, scalable framework that can be used to achieve optimal entanglement distribution within crossbar quantum networks, this study offers a theoretical achievement which can be also used for enhancing quantum network performance. An algorithm for selecting an optimal entanglement distribution configuration is proposed and fully tested on realistic possible configurations.

Crossed Andreev Reflection and Elastic Cotunneling in Three Quantum Dots Coupled by Superconductors

The formation of a topological superconducting phase in a quantum-dot-based Kitaev chain requires nearest neighbor crossed Andreev reflection and elastic cotunneling. Here, we report on a hybrid InSb nanowire in a three-site Kitaev chain geometry-the smallest system with well-defined bulk and edge-where two superconductor-semiconductor hybrids separate three quantum dots. We demonstrate pairwise crossed Andreev reflection and elastic cotunneling between both pairs of neighboring dots and show sequential tunneling processes involving all three quantum dots. These results are the next step toward the realization of topological superconductivity in long Kitaev chain devices with many coupled quantum dots.

Analysis of continuous-variable quantum teleportation enhanced by measurement-based noiseless quantum amplification

Continuous-variable quantum teleportation enables deterministic teleportation of quantum states of optical modes. However, the state transfer is imperfect and limited by the amount of squeezing in the shared two-mode entangled state. Recently, it has been proposed and experimentally demonstrated that the performance of continuous-variable teleportation can be conditionally improved using a measurement-based noiseless quantum amplification [J. Zhao et al., Nat. Commun.14, 4745 (2023)10.1038/s41467-023-40438-z]. An inverse Gaussian filter with sufficiently high cut-off is applied to outcomes of the continuous-variable Bell measurement, which can increase the fidelity of state teleportation and the cost of making the protocol probabilistic. Here we provide a detailed theoretical analysis of this protocol and discuss its effects and limitations. We focus on teleportation of classes of Gaussian states with fixed covariance matrix and variable displacement. The measurement-based noiseless amplification conditionally improves the precision of estimation of the coherent displacement of the teleported state from the outcomes of continuous-variable Bell measurement. Therefore, more information about the teleported state is revealed and unity-gain teleportation becomes possible with a lower added thermal noise as compared to deterministic teleportation.

Entangled-Based Quantum Wavelength-Division-Multiplexing and Multiple-Access Networks

This paper investigates the mathematical model of the quantum wavelength-division-multiplexing (WDM) network based on the entanglement distribution with the least required wavelengths and passive devices. By adequately utilizing wavelength multiplexers, demultiplexers, and star couplers, N wavelengths are enough to distribute the entanglement among each pair of N users. Moreover, the number of devices employed is reduced by substituting a waveguide grating router for multiplexers and demultiplexers. Furthermore, this study examines implementing the BBM92 quantum key distribution in an entangled-based quantum WDM network. The proposed scheme in this paper may be applied to potential applications such as teleportation in entangled-based quantum WDM networks.

Telecom-band quantum dot technologies for long-distance quantum networks

A future quantum internet is expected to generate, distribute, store and process quantum bits (qubits) over the world by linking different quantum nodes via quantum states of light. To facilitate long-haul operations, quantum repeaters must operate at telecom wavelengths to take advantage of both the low-loss optical fibre network and the established technologies of modern optical communications. Semiconductor quantum dots have thus far shown exceptional performance as key elements for quantum repeaters, such as quantum light sources and spin-photon interfaces, but only in the near-infrared regime. Therefore, the development of high-performance telecom-band quantum dot devices is highly desirable for a future solid-state quantum internet based on fibre networks. In this Review, we present the physics and technological developments towards epitaxial quantum dot devices emitting in the telecom O- and C-bands for quantum networks, considering both advanced epitaxial growth for direct telecom emission and quantum frequency conversion for telecom-band down-conversion of near-infrared quantum dot devices. We also discuss the challenges and opportunities for future realization of telecom quantum dot devices with improved performance and expanded functionality through hybrid integration.

Percolation Theories for Quantum Networks

Quantum networks have experienced rapid advancements in both theoretical and experimental domains over the last decade, making it increasingly important to understand their large-scale features from the viewpoint of statistical physics. This review paper discusses a fundamental question: how can entanglement be effectively and indirectly (e.g., through intermediate nodes) distributed between distant nodes in an imperfect quantum network, where the connections are only partially entangled and subject to quantum noise? We survey recent studies addressing this issue by drawing exact or approximate mappings to percolation theory, a branch of statistical physics centered on network connectivity. Notably, we show that the classical percolation frameworks do not uniquely define the network's indirect connectivity. This realization leads to the emergence of an alternative theory called "concurrence percolation", which uncovers a previously unrecognized quantum advantage that emerges at large scales, suggesting that quantum networks are more resilient than initially assumed within classical percolation contexts, offering refreshing insights into future quantum network design.

Optimal Estimation of Quantum Coherence by Bell State Measurement: A Case Study

Quantum coherence is the most distinguished feature of quantum mechanics. As an important resource, it is widely applied to quantum information technologies, including quantum algorithms, quantum computation, quantum key distribution, and quantum metrology, so it is important to develop tools for efficient estimation of the coherence. Bell state measurement plays an important role in quantum information processing. In particular, it can also, as a two-copy collective measurement, directly measure the quantum coherence of an unknown quantum state in the experiment, and does not need any optimization procedures, feedback, or complex mathematical calculations. In this paper, we analyze the performance of estimating quantum coherence with Bell state measurement for a qubit case from the perspective of semiparametric estimation and single-parameter estimation. The numerical results show that Bell state measurement is the optimal measurement for estimating several frequently-used coherence quantifiers, and it has been demonstrated in the perspective of the quantum limit of semiparametric estimation and Fisher information.

Entanglement and indistinguishability: facing some challenges from a new perspective

While entanglement in the case of distinguishable particles is clearly understood, in the case of indistinguishable particles, there is still a wide debate regarding basic conceptual issues. Here, I will address two such issues. First, the debate almost always rests on a differentiated treatment of the cases of distinguishability and indistinguishability, even with respect to the definition of the concept of entanglement. Second, the fact that symmetrized and antisymmetrized states of indistinguishable particles are non-factorizable leads to certain perplexities about the very nature of entanglement. In the present work, both issues will be addressed from the perspective of an ontology of properties, which finds its natural expression in the algebraic formalism of quantum mechanics. The final goal will be to show that the proposed ontology allows a unified treatment of entanglement in the distinguishability and indistinguishability cases and offers a straightforward way out to perplexities. This article is part of the theme issue 'Identity, individuality and indistinguishability in physics and mathematics'.

Insecurity of Quantum Blockchains Based on Entanglement in Time

In this study, the security implications of utilizing the concept of entanglement in time in the quantum representation of a blockchain data structure are investigated. The analysis reveals that the fundamental idea underlying this representation relies on an uncertain interpretation of experimental results. A different perspective is provided by adopting the Copenhagen interpretation, which explains the observed correlations in the experiment without invoking the concept of entanglement in time. According to this interpretation, the qubits responsible for these correlations are not entangled, posing a challenge to the security foundation of the data structure. The study incorporates theoretical analysis, numerical simulations, and experiments using real quantum hardware. By employing a dedicated circuit for detecting genuine entanglement, the existence of entanglement in the process of generating a quantum blockchain is conclusively excluded.

Entanglement Parallelization via Quantum Fourier Transform

In this study, a technique based on the quantum Fourier transform (QFT) that allows the generation of disjoint sets of entangled particles is presented, in such a way that particles of the same set are entangled with each other, while particles of different sets are completely independent. Several applications of this technique are implemented on three physical platforms, of 5 (Belem), 7 (Oslo), and 14 (Melbourne) qubits, of the international business machine (IBM Q) quantum experience program, where all these applications are specially selected due to their particular commitment to the future Quantum Internet.

Optimal quantum network decongestion strategies

This study clarifies the problem of decongestion in quantum networks, with a specific focus on the crucial task of entanglement distribution. Entangled particles are a valuable resource in quantum networks, as they are used for most quantum protocols. As such, ensuring that nodes in quantum networks are supplied with entanglement efficiently is mandatory. Many times, parts of a quantum network are contested by multiple entanglement resupply processes and the distribution of entanglement becomes a challenge. The most common network intersection topology, the star-shape and it's various generalizations, are analyzed, and effective decongestion strategies, in order to achieve optimal entanglement distribution, are proposed. The analysis is comprehensive and relies on rigorous mathematical calculations which aids in selecting the most appropriate strategy for different scenarios optimally.

Optimal High-Dimensional Entanglement Concentration for Pure Bipartite Systems

Considering pure quantum states, entanglement concentration is the procedure where, from N copies of a partially entangled state, a single state with higher entanglement can be obtained. Obtaining a maximally entangled state is possible for N=1. However, the associated success probability can be extremely low when increasing the system's dimensionality. In this work, we study two methods to achieve a probabilistic entanglement concentration for bipartite quantum systems with a large dimensionality for N=1, regarding a reasonably good probability of success at the expense of having a non-maximal entanglement. Firstly, we define an efficiency function Q considering a tradeoff between the amount of entanglement (quantified by the I-Concurrence) of the final state after the concentration procedure and its success probability, which leads to solving a quadratic optimization problem. We found an analytical solution, ensuring that an optimal scheme for entanglement concentration can always be found in terms of Q. Finally, a second method was explored, which is based on fixing the success probability and searching for the maximum amount of entanglement attainable. Both ways resemble the Procrustean method applied to a subset of the most significant Schmidt coefficients but obtaining non-maximally entangled states.

Distilling Nonlocality in Quantum Correlations

Nonlocality, as established by the seminal Bell's theorem, is considered to be the most striking feature of correlations present in spacelike separated events. Its practical application in device independent protocols, such as secure key distribution, randomness certification, etc., demands identification and amplification of such correlations observed in the quantum world. In this Letter we study the prospect of nonlocality distillation, wherein, by applying a natural set of free operations (called wirings) on many copies of weakly nonlocal systems, one aims to generate correlations of higher nonlocal strength. In the simplest Bell scenario, we identify a protocol, namely, logical OR-AND wiring, that can distill nonlocality to a significantly high degree starting from arbitrarily weak quantum nonlocal correlations. As it turns out, our protocol has several interesting facets: (i) it demonstrates that a set of distillable quantum correlations has nonzero measure in the full eight-dimensional correlation space, (ii) it can distill quantum Hardy correlations by preserving its structure, (iii) it shows that (nonlocal) quantum correlations sufficiently close to the local deterministic points can be distilled by a significant amount. Finally, we also demonstrate efficacy of the considered distillation protocol in detecting postquantum correlations.

Optimal entanglement distribution policies in homogeneous repeater chains with cutoffs

We study the limits of bipartite entanglement distribution using a chain of quantum repeaters that have quantum memories. To generate end-to-end entanglement, each node can attempt the generation of an entangled link with a neighbor, or perform an entanglement swapping measurement. A maximum storage time, known as cutoff, is enforced on the memories to ensure high-quality entanglement. Nodes follow a policy that determines when to perform each operation. Global-knowledge policies take into account all the information about the entanglement already produced. Here, we find global-knowledge policies that minimize the expected time to produce end-to-end entanglement. Our methods are based on Markov decision processes and value and policy iteration. We compare optimal policies to a policy in which nodes only use local information. We find that the advantage in expected delivery time provided by an optimal global-knowledge policy increases with increasing number of nodes and decreasing probability of successful swapping.

Synchronization and coexistence in quantum networks

We investigate the coexistence of clock synchronization protocols with quantum signals in a common single-mode optical fiber. By measuring optical noise between 1500 nm to 1620 nm we demonstrate a potential for up to 100 quantum, 100 GHz wide channels coexisting with the classical synchronization signals. Both "White Rabbit" and pulsed laser-based synchronization protocols were characterized and compared. We establish a theoretical limit of the fiber link length for coexisting quantum and classical channels. The maximal fiber length is below approximately 100 km for off-the-shelf optical transceivers and can be significantly improved by taking advantage of quantum receivers.

Entanglement Swapping and Swapped Entanglement

Entanglement swapping is gaining widespread attention due to its application in entanglement distribution among different parts of quantum appliances. We investigate the entanglement swapping for pure and noisy systems, and argue different entanglement quantifiers for quantum states. We explore the relationship between the entanglement of initial states and the average entanglement of final states in terms of concurrence and negativity. We find that if initial quantum states are maximally entangled and we make measurements in the Bell basis, then average concurrence and average negativity of final states give similar results. In this case, we simply obtain the average concurrence (average negativity) of the final states by taking the product of concurrences (negativities) of the initial states. However, the measurement in non-maximally entangled basis during entanglement swapping degrades the average swapped entanglement. Further, the product of the entanglement of the initial mixed states provides an upper bound to the average swapped entanglement of final states obtained after entanglement swapping. The negativity work well for weak entangled noisy states but concurrence gives better results for relatively strong entanglement regimes. We also discuss how successfully the output state can be used as a channel for the teleportation of an unknown qubit.

Experimental Mode-Pairing Measurement-Device-Independent Quantum Key Distribution without Global Phase Locking

In the past two decades, quantum key distribution networks based on telecom fibers have been implemented on metropolitan and intercity scales. One of the bottlenecks lies in the exponential decay of the key rate with respect to the transmission distance. Recently proposed schemes mainly focus on achieving longer distances by creating a long-arm single-photon interferometer over two communication parties. Despite their advantageous performance over long communication distances, the requirement of phase locking between two remote lasers is technically challenging. By adopting the recently proposed mode-pairing idea, we realize high-performance quantum key distribution without global phase locking. Using two independent off-the-shelf lasers, we show a quadratic key-rate improvement over the conventional measurement-device-independent schemes in the regime of metropolitan and intercity distances. For longer distances, we also boost the key rate performance by 3 orders of magnitude via 304 km commercial fiber and 407 km ultralow-loss fiber. We expect this ready-to-implement high-performance scheme to be widely used in future intercity quantum communication networks.

Dynamics of Quantum Networks in Noisy Environments

Noise exists inherently in realistic quantum systems and affects the evolution of quantum systems. We investigate the dynamics of quantum networks in noisy environments by using the fidelity of the quantum evolved states and the classical percolation theory. We propose an analytical framework that allows us to characterize the stability of quantum networks in terms of quantum noises and network topologies. The calculation results of the framework determine the maximal time that quantum networks with different network topologies can maintain the ability to communicate under noise. We demonstrate the results of the framework through examples of specific graphs under amplitude damping and phase damping noises. We further consider the capacity of the quantum network in a noisy environment according to the proposed framework. The analytical framework helps us better understand the evolution time of a quantum network and provides a reference for designing large quantum networks.

Perspectives on determinism in quantum mechanics: Born, Bohm, and the "Quantal Newtonian" laws

Quantum mechanics has a deterministic Schrödinger equation for the wave function. The Göttingen-Copenhagen statistical interpretation is based on the Born Rule that interprets the wave function as a "probability amplitude." A precept of this interpretation is the lack of determinism in quantum mechanics. The Bohm interpretation is that the wave function is a source of a field experienced by the electrons, thereby attributing determinism to quantum theory. In this paper, we present a new perspective on such determinism. The ideas are based on the equations of motion or "Quantal Newtonian" Laws obeyed by each electron. These Laws, derived from the temporal and stationary-state Schrödinger equation, are interpreted in terms of "classical" fields whose sources are quantal expectations of Hermitian operators taken with respect to the wave function. According to the Second Law, each electron experiences an external field-the quantal Coulomb-Lorentz law. It also experiences an internal field representative of properties of the system: correlations due to Coulomb repulsion and Pauli principle; the density; kinetic effects; and an internal magnetic field component. There is a response field. The First Law states that the sum of the external and internal fields experienced by each electron vanishes. These fields are akin to those of classical physics: They pervade all space; their structure is descriptive of the quantum system; the energy of the system is stored in these fields. It is in the classical behavior of these fields, which arise from quantal sources that one may then speak of determinism in quantum mechanics.

The deep space quantum link: prospective fundamental physics experiments using long-baseline quantum optics

The National Aeronautics and Space Administration's Deep Space Quantum Link mission concept enables a unique set of science experiments by establishing robust quantum optical links across extremely long baselines. Potential mission configurations include establishing a quantum link between the Lunar Gateway moon-orbiting space station and nodes on or near the Earth. This publication summarizes the principal experimental goals of the Deep Space Quantum Link. These goals, identified through a multi-year design study conducted by the authors, include long-range teleportation, tests of gravitational coupling to quantum states, and advanced tests of quantum nonlocality.

Four-dimensional orbital angular momentum Bell-state measurement assisted by the auxiliary polarization and path degrees of freedom

The orbital angular momentum (OAM) carried by twisted photons provides a promising playground for high-dimensional quantum information processing. While Bell-state measurement is the cornerstone for various quantum information applications, the deterministic discrimination of the complete high-dimensional Bell states with linear optics remains relatively unexplored in the OAM state space. Here, we demonstrate a theoretical scheme for the complete four-dimensional OAM Bell-state measurement by using the single-photon hyperentangled state analyzer, in which the auxiliary two-dimensional polarization entanglement and two-dimensional path entanglement are utilized. Our scheme offers an alternative route toward enhancing the channel capacity in quantum communication and increasing the robustness against deleterious noise in practical experiments with twisted photons.

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.

Entanglement Swapping and Quantum Correlations via Symmetric Joint Measurements

We use hyperentanglement to experimentally realize deterministic entanglement swapping based on quantum elegant joint measurements. These are joint projections of two qubits onto highly symmetric, isoentangled bases. We report measurement fidelities no smaller than 97.4%. We showcase the applications of these measurements by using the entanglement swapping procedure to demonstrate quantum correlations in the form of proof-of-principle violations of both bilocal Bell inequalities and more stringent correlation criteria corresponding to full network nonlocality. Our results are a foray into entangled measurements and nonlocality beyond the paradigmatic Bell state measurement and they show the relevance of more general measurements in entanglement swapping scenarios.

Mode-pairing quantum key distribution

Quantum key distribution — the establishment of information-theoretically secure keys based on quantum physics — is mainly limited by its practical performance, which is characterised by the dependence of the key rate on the channel transmittance R(η). Recently, schemes based on single-photon interference have been proposed to improve the key rate to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R=O(\sqrt{\eta })$$\end{document}R=O(η) by overcoming the point-to-point secret key capacity bound with interferometers. Unfortunately, all of these schemes require challenging global phase locking to realise a stable long-arm single-photon interferometer with a precision of approximately 100 nm over fibres that are hundreds of kilometres long. Aiming to address this problem, we propose a mode-pairing measurement-device-independent quantum key distribution scheme in which the encoded key bits and bases are determined during data post-processing. Using conventional second-order interference, this scheme can achieve a key rate of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R=O(\sqrt{\eta })$$\end{document}R=O(η) without global phase locking when the local phase fluctuation is mild. We expect this high-performance scheme to be ready-to-implement with off-the-shelf optical devices.

Measurement-device-independent QKD schemes suffer from a trade-off between ease of implementation (avoiding the need for global phase locking) and high rates (quadratic improvement in rate). Here, the authors propose a protocol which offers both simple implementation and strong performances.

Entangling single atoms over 33 km telecom fibre

Quantum networks promise to provide the infrastructure for many disruptive applications, such as efficient long-distance quantum communication and distributed quantum computing1,2. Central to these networks is the ability to distribute entanglement between distant nodes using photonic channels. Initially developed for quantum teleportation3,4 and loophole-free tests of Bell's inequality5,6, recently, entanglement distribution has also been achieved over telecom fibres and analysed retrospectively7,8. Yet, to fully use entanglement over long-distance quantum network links it is mandatory to know it is available at the nodes before the entangled state decays. Here we demonstrate heralded entanglement between two independently trapped single rubidium atoms generated over fibre links with a length up to 33 km. For this, we generate atom-photon entanglement in two nodes located in buildings 400 m line-of-sight apart and to overcome high-attenuation losses in the fibres convert the photons to telecom wavelength using polarization-preserving quantum frequency conversion9. The long fibres guide the photons to a Bell-state measurement setup in which a successful photonic projection measurement heralds the entanglement of the atoms10. Our results show the feasibility of entanglement distribution over telecom fibre links useful, for example, for device-independent quantum key distribution11-13 and quantum repeater protocols. The presented work represents an important step towards the realization of large-scale quantum network links.

Deterministic Entanglement Swapping with Hybrid Discrete- and Continuous-Variable Systems

The study of entanglement between discrete and continuous variables is an important theoretical and experimental topic in quantum information processing, for which entanglement swapping is one of the interesting elements. Entanglement swapping allows two particles without interacting with each other in any way, to form an entangled state by the action of another pair of entangled particles. In this paper, we propose an experimentally feasible scheme to realize deterministic entanglement swapping in the hybrid system with discrete and continuous variables. The process is achieved by preparing two pairs of entangled states, each is formed by a qubit and two quasi-orthogonal coherent state elements of a cavity, performing a Bell-state analysis through nonlocal operations on the continuous variable states of the two cavities, and projecting the two qubits into a maximally entangled state. The present scheme may be applied to other physical systems sustaining such hybrid discrete and continuous forms, providing a typical paradigm for entanglement manipulation through deterministic swapping operations.

Quantum Nonlocality in Any Forked Tree-Shaped Network

In the last decade, much attention has been focused on examining the nonlocality of various quantum networks, which are fundamental for long-distance quantum communications. In this paper, we consider the nonlocality of any forked tree-shaped network, where each node, respectively, shares arbitrary number of bipartite sources with other nodes in the next “layer”. The Bell-type inequalities for such quantum networks are obtained, which are, respectively, satisfied by all (tn−1)-local correlations and all local correlations, where tn denotes the total number of nodes in the network. The maximal quantum violations of these inequalities and the robustness to noise in these networks are also discussed. Our network can be seen as a generalization of some known quantum networks.

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.

Experimental demonstration of free-space two-photon interference

Quantum interference plays an essential role in understanding the concepts of quantum physics. Moreover, the interference of photons is indispensable for large-scale quantum information processing. With the development of quantum networks, interference of photons transmitted through long-distance fiber channels has been widely implemented. However, quantum interference of photons using free-space channels is still scarce, mainly due to atmospheric turbulence. Here, we report an experimental demonstration of Hong-Ou-Mandel interference with photons transmitted by free-space channels. Two typical photon sources, i.e., correlated photon pairs generated in spontaneous parametric down conversion (SPDC) process and weak coherent states, are employed. A visibility of 0.744 ± 0.013 is observed by interfering with two photons generated in the SPDC process, exceeding the classical limit of 0.5. Our results demonstrate that the quantum property of photons remains even after transmission through unstable free-space channels, indicating the feasibility and potential application of free-space-based quantum interference in quantum information processing.

Heralding Multiple Photonic Pulsed Bell Pairs via Frequency-Resolved Entanglement Swapping

Entanglement is a unique property of quantum systems and an essential resource for many quantum technologies. The ability to transfer or swap entanglement between systems is an important protocol in quantum information science. Entanglement swapping between photons forms the basis of distributed quantum networks. Here an experiment demonstrating entanglement swapping from two independent multimode time-frequency entangled sources is presented, resulting in multiple heralded frequency-mode Bell states. Entanglement in the heralded states is verified by measuring conditional anticorrelated joint spectra and quantum beating in two-photon interference. Our experiment heralds up to five orthogonal Bell pairs within the same setup, and this number is ultimately limited only by the entanglement of the initial sources.

All-Optical Entanglement Swapping

Entanglement swapping, which is a core component of quantum network and an important platform for testing the foundation of quantum mechanics, can enable the entangling of two independent particles without direct interaction both in discrete variable and continuous variable systems. Conventionally, the realization of entanglement swapping relies on the Bell-state measurement. In particular, for entanglement swapping in continuous variable regime, such Bell-state measurement involves the optic-electro and electro-optic conversion, which limits the applications of the entanglement swapping for constructing broadband quantum network. In this Letter, we propose and demonstrate a measurement-free all-optical entanglement swapping. In our scheme, a high-gain parametric amplifier based on the four-wave mixing process is exploited to realize the function of Bell-state measurement without detection, which avoids the introduction of the optic-electro and electro-optic conversion. Our results provide an all-optical paradigm for implementing entanglement swapping and pave the way to construct a measurement-free all-optical broadband quantum network.

Entanglement and indistinguishability in a quantum ontology of properties

The aim of the present article is to address the problem of entanglement in the case of indistinguishable particles from a perspective based on the algebraic formalism of quantum mechanics, which is the natural formal counterpart of an ontology of properties, devoid of the ontological category of object. On the basis of this perspective, an algebraic definition of entanglement is adopted, which supplies a unified conception, valid for both the distinguishable and the indistinguishable cases. An additional advantage of this algebraic definition is that it does justice to the relativity of entanglement, a feature that cannot be ignored.

Ruling Out Real-Valued Standard Formalism of Quantum Theory

Standard quantum theory was formulated with complex-valued Schrödinger equations, wave functions, operators, and Hilbert spaces. Previous work attempted to simulate quantum systems using only real numbers by exploiting an enlarged Hilbert space. A fundamental question arises: are the complex numbers really necessary in the standard formalism of quantum theory? To answer this question, a quantum game has been developed to distinguish standard quantum theory from its real-number analog, by revealing a contradiction between a high-fidelity multiqubit quantum experiment and players using only real-number quantum theory. Here, using superconducting qubits, we faithfully realize the quantum game based on deterministic entanglement swapping with a state-of-the-art fidelity of 0.952. Our experimental results violate the real-number bound of 7.66 by 43 standard deviations. Our results disprove the real-number formulation and establish the indispensable role of complex numbers in the standard quantum theory.

Testing Real Quantum Theory in an Optical Quantum Network

Quantum theory is commonly formulated in complex Hilbert spaces. However, the question of whether complex numbers need to be given a fundamental role in the theory has been debated since its pioneering days. Recently it has been shown that tests in the spirit of a Bell inequality can reveal quantum predictions in entanglement swapping scenarios that cannot be modeled by the natural real-number analog of standard quantum theory. Here, we tailor such tests for implementation in state-of-the-art photonic systems. We experimentally demonstrate quantum correlations in a network of three parties and two independent EPR sources that violate the constraints of real quantum theory by over 4.5 standard deviations, hence disproving real quantum theory as a universal physical theory.

Full Network Nonlocality

Networks have advanced the study of nonlocality beyond Bell's theorem. Here, we introduce the concept of full network nonlocality, which describes correlations that necessitate all links in a network to distribute nonlocal resources. Showcasing that this notion is stronger than standard network nonlocality, we prove that the most well-known network Bell test does not witness full network nonlocality. In contrast, we demonstrate that its generalization to star networks is capable of detecting full network nonlocality in quantum theory. More generally, we point out that established methods for analyzing local and theory-independent correlations in networks can be combined in order to systematically deduce sufficient conditions for full network nonlocality in any network and input-output scenario. We demonstrate the usefulness of these methods by constructing polynomial witnesses of full network nonlocality for the bilocal scenario. Then, we show that these inequalities can be violated via quantum elegant joint measurements.

Hybrid Entanglement between Optical Discrete Polarizations and Continuous Quadrature Variables

By coherently combining advantages while largely avoiding limitations of two mainstream platforms, optical hybrid entanglement involving both discrete and continuous variables has recently garnered widespread attention and emerged as a promising idea for building heterogenous quantum networks. In contrast to previous results, here we propose a new scheme to remotely generate hybrid entanglement between discrete polarization and continuous quadrature optical qubits heralded by two-photon Bell-state measurement. As a novel nonclassical light resource, we further use it to discuss two examples of ways—entanglement swapping and quantum teleportation—in which quantum information processing and communications could make use of this hybrid technique.

Lightweight mediated semi-quantum key distribution protocol with a dishonest third party based on Bell states

The mediated semi-quantum key distribution (MSQKD) protocol is an important research issue that lets two classical participants share secret keys securely between each other with the help of a third party (TP). However, in the existing MSQKD protocols, there are two improvable issues, namely (1) the classical participants must be equipped with expensive detectors to avoid Trojan horse attacks and (2) the trustworthiness level of TP must be honest. To the best of our knowledge, none of the existing MSQKD protocols can resolve both these issues. Therefore, this study takes Bell states as the quantum resource to propose a MSQKD protocol, in which the classical participants do not need a Trojan horse detector and the TP is dishonest. Furthermore, the proposed protocol is shown to be secure against well-known attacks and the classical participants only need two quantum capabilities. Therefore, in comparison to the existing MSQKD protocols, the proposed protocol is better practical.

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.

Vulnerability of Satellite Quantum Key Distribution to Disruption from Ground-Based Lasers

Satellite-mediated quantum key distribution (QKD) is set to become a critical technology for quantum-secure communication over long distances. While satellite QKD cannot be effectively eavesdropped, we show it can be disrupted (or ‘jammed’) with relatively simple and readily available equipment. We developed an atmospheric attenuation and satellite optical scattering model to estimate the rate of excess noise photons that can be injected into a satellite QKD channel by an off-axis laser, and calculated the effect this added noise has on the quantum bit error rate. We show that a ground-based laser on the order of 1 kW can significantly disrupt modern satellite QKD systems due to photons scattering off the satellite being detected by the QKD receiver on the ground. This class of laser can be purchased commercially, meaning such a method of disruption could be a serious threat to effectively securing high-value communications via satellite QKD in the future. We also discuss these results in relation to likely future developments in satellite-mediated QKD systems, and countermeasures that can be taken against this, and related methods, of disruption.

Network Quantum Steering

The development of large-scale quantum networks promises to bring a multitude of technological applications as well as shed light on foundational topics, such as quantum nonlocality. It is particularly interesting to consider scenarios where sources within the network are statistically independent, which leads to so-called network nonlocality, even when parties perform fixed measurements. Here we promote certain parties to be trusted and introduce the notion of network steering and network local hidden state (NLHS) models within this paradigm of independent sources. In one direction, we show how the results from Bell nonlocality and quantum steering can be used to demonstrate network steering. We further show that it is a genuinely novel effect by exhibiting unsteerable states that nevertheless demonstrate network steering based upon entanglement swapping yielding a form of activation. On the other hand, we provide no-go results for network steering in a large class of scenarios by explicitly constructing NLHS models.

Genuine Multipartite Nonlocality with Causal-Diagram Postselection

The generation and verification of genuine multipartite nonlocality (GMN) is of central interest for both fundamental research and quantum technological applications, such as quantum privacy. To demonstrate GMN in measurement data, the statistics are commonly postselected by neglecting undesired data. Until now, valid postselection strategies have been restricted to local postselection. A general postselection that is decided after communication between parties can mimic nonlocality, even though the complete data are local. Here, we establish conditions under which GMN is demonstrable even if observations are postselected collectively. Intriguingly, certain postselection strategies that require communication among several parties still offer a demonstration of GMN shared between all parties. The results are derived using the causal structure of the experiment and the no-signaling condition imposed by relativity. Finally, we apply our results to show that genuine three-partite nonlocality can be created with independent particle sources.

Catalytic Quantum Teleportation

In this work, we address fundamental limitations of quantum teleportation-the process of transferring quantum information using classical communication and preshared entanglement. We develop a new teleportation protocol based upon the idea of using ancillary entanglement catalytically, i.e., without depleting it. This protocol is then used to show that catalytic entanglement allows for a noiseless quantum channel to be simulated with a quality that could never be achieved using only entanglement from the shared state, even for catalysts with a small dimension. On the one hand, this allows for a more faithful transmission of quantum information using generic states and fixed amount of consumed entanglement. On the other hand, this shows, for the first time, that entanglement catalysis provides a genuine advantage in a generic quantum-information processing task. Finally, we show that similar ideas can be directly applied to study quantum catalysis for more general problems in quantum mechanics. As an application, we show that catalysts can activate so-called passive states, a concept that finds widespread application, e.g., in quantum thermodynamics.

Quantum discord of thermal two-photon orbital angular momentum state: mimicking teleportation to transmit an image

We formulate a density matrix to fully describe two-photon state within a thermal light source in the photon orbital angular momentum (OAM) Hilbert space. We prove the separability, i.e., zero entanglement of the thermal two-photon state. Still, we reveal the hidden quantum correlations in terms of geometric measures of discord. By mimicking the original protocol of quantum teleportation, we demonstrate that the non-zero quantum discord can be utilized to transmit a high-dimensional OAM state at the single-photon level. It is found that albeit the low fidelity of teleportation due to the inherent component of maximally mixed state, the information of all parameters that characterize the original state can still be extracted from the teleported one. Besides, we demonstrate that the multiple repetitions of the protocol, enable the transmission of a complex-amplitude light field, e.g., an optical image, regardless of being accompanied with a featureless background. We also distinguish our scheme of optical image transmission from that of ghost imaging.

Switching and Swapping of Quantum Information: Entropy and Entanglement Level

Information switching and swapping seem to be fundamental elements of quantum communication protocols. Another crucial issue is the presence of entanglement and its level in inspected quantum systems. In this article, a formal definition of the operation of the swapping local quantum information and its existence proof, together with some elementary properties analysed through the prism of the concept of the entropy, are presented. As an example of the local information swapping usage, we demonstrate a certain realisation of the quantum switch. Entanglement levels, during the work of the switch, are calculated with the Negativity measure and a separability criterion based on the von Neumann entropy, spectral decomposition and Schmidt decomposition. Results of numerical experiments, during which the entanglement levels are estimated for systems under consideration with and without distortions, are presented. The noise is generated by the Dzyaloshinskii-Moriya interaction and the intrinsic decoherence is modelled by the Milburn equation. This work contains a switch realisation in a circuit form-built out of elementary quantum gates, and a scheme of the circuit which estimates levels of entanglement during the switch's operating.

Bilocal Bell Inequalities Violated by the Quantum Elegant Joint Measurement

Network Bell experiments give rise to a form of quantum nonlocality that conceptually goes beyond Bell's theorem. We investigate here the simplest network, known as the bilocality scenario. We depart from the typical use of the Bell state measurement in the network central node and instead introduce a family of symmetric isoentangled measurement bases that generalize the so-called "elegant joint measurement." This leads us to report noise-tolerant quantum correlations that elude bilocal variable models. Inspired by these quantum correlations, we introduce network Bell inequalities for the bilocality scenario and show that they admit noise-tolerant quantum violations. In contrast to many previous studies of network Bell inequalities, neither our inequalities nor their quantum violations are based on standard Bell inequalities and standard quantum nonlocality. Moreover, we pave the way for an experimental realization by presenting a simple two-qubit quantum circuit for the implementation of the elegant joint measurement and our generalization.