Heralded entanglement between widely separated atoms

Entanglement of nanophotonic quantum memory nodes in a telecom network

A key challenge in realizing practical quantum networks for long-distance quantum communication involves robust entanglement between quantum memory nodes connected by fibre optical infrastructure1-3. Here we demonstrate a two-node quantum network composed of multi-qubit registers based on silicon-vacancy (SiV) centres in nanophotonic diamond cavities integrated with a telecommunication fibre network. Remote entanglement is generated by the cavity-enhanced interactions between the electron spin qubits of the SiVs and optical photons. Serial, heralded spin-photon entangling gate operations with time-bin qubits are used for robust entanglement of separated nodes. Long-lived nuclear spin qubits are used to provide second-long entanglement storage and integrated error detection. By integrating efficient bidirectional quantum frequency conversion of photonic communication qubits to telecommunication frequencies (1,350 nm), we demonstrate the entanglement of two nuclear spin memories through 40 km spools of low-loss fibre and a 35-km long fibre loop deployed in the Boston area urban environment, representing an enabling step towards practical quantum repeaters and large-scale quantum networks.

Creation of memory-memory entanglement in a metropolitan quantum network

Towards realizing the future quantum internet1,2, a pivotal milestone entails the transition from two-node proof-of-principle experiments conducted in laboratories to comprehensive multi-node set-ups on large scales. Here we report the creation of memory-memory entanglement in a multi-node quantum network over a metropolitan area. We use three independent memory nodes, each of which is equipped with an atomic ensemble quantum memory3 that has telecom conversion, together with a photonic server where detection of a single photon heralds the success of entanglement generation. The memory nodes are maximally separated apart for 12.5 kilometres. We actively stabilize the phase variance owing to fibre links and control lasers. We demonstrate concurrent entanglement generation between any two memory nodes. The memory lifetime is longer than the round-trip communication time. Our work provides a metropolitan-scale testbed for the evaluation and exploration of multi-node quantum network protocols and starts a stage of quantum internet research.

Photonic Which-Path Entangler Based on Longitudinal Cavity-Qubit Coupling

We show that a modulated longitudinal cavity-qubit coupling can be used to control the path taken by a multiphoton coherent-state wave packet conditioned on the state of a qubit, resulting in a qubit-which-path (QWP) entangled state. QWP states can generate long-range multipartite entanglement using strategies for interfacing discrete- and continuous-variable degrees of freedom. Using the approach presented here, entanglement can be distributed in a quantum network without the need for single-photon sources or detectors.

Steady motional entanglement between two distant levitated nanoparticles

Quantum entanglement in macroscopic systems is not only essential for practical quantum information processing, but also valuable for the study of the boundary between quantum and the classical world. However, it is very challenging to achieve the steady remote entanglement between distant macroscopic systems. We consider two distant nanoparticles, both of which are optically trapped in two cavities. Based on the coherent scattering mechanism, we find that the ultrastrong optomechanical coupling between the cavity modes and the motion of the levitated nanoparticles could be achieved. The large and steady entanglement between the filtered output cavity modes and the motion of nanoparticles can be generated if the trapping laser is under the red sideband. Then through entanglement swapping, the steady motional entanglement between the distant nanoparticles can be realized. We numerically simulate and find that the two nanoparticles with 10 km distance can be entangled for the experimentally feasible parameters, even in room temperature environments. The generated continuous variable multipartite entanglement is the key to realizing the quantum enhanced sensor network and the sensitivity beyond the standard quantum limit.

Quantum storage of entangled photons at telecom wavelengths in a crystal

Quantum storage and distribution of entanglement are the key ingredients for realizing a global quantum internet. Compatible with existing fiber networks, telecom-wavelength entangled photons and corresponding quantum memories are of central interest. Recently, 167Er3+ ions have been identified as a promising candidate for an efficient telecom quantum memory. However, to date, no storage of entangled photons, the crucial step of quantum memory using these promising ions, 167Er3+, has been reported. Here, we demonstrate the storage and retrieval of the entangled state of two telecom photons generated from an integrated photonic chip. Combining the natural narrow linewidth of the entangled photons and long storage time of 167Er3+ ions, we achieve storage time of 1.936 μs, more than 387 times longer than in previous works. Successful storage of entanglement in the crystal is certified using entanglement witness measurements. These results pave the way for realizing quantum networks based on solid-state devices.

Meterscale Strong Coupling between Magnons and Photons

We experimentally realize a meterscale strong coupling effect between magnons and photons at room temperature, with a coherent coupling of ∼20  m and a dissipative coupling of ∼7.6  m. To this end, we integrate a saturable gain into a microwave cavity and then couple this active cavity to a magnon mode via a long coaxial cable. The gain compensates for the cavity dissipation, but preserves the cavity radiation that mediates the indirect photon-magnon coupling. It thus enables the long-range strong photon-magnon coupling. With full access to traveling waves, we demonstrate a remote control of photon-magnon coupling by modulating the phase and amplitude of traveling waves, rather than reconfiguring subsystems themselves. Our method for realizing long-range strong coupling in cavity magnonics provides a general idea for other physical systems. Our experimental achievements may promote the construction of information networks based on cavity magnonics.

Telecom-Wavelength Quantum Repeater Node Based on a Trapped-Ion Processor

A quantum repeater node is presented based on trapped ions that act as single-photon emitters, quantum memories, and an elementary quantum processor. The node's ability to establish entanglement across two 25-km-long optical fibers independently, then to swap that entanglement efficiently to extend it over both fibers, is demonstrated. The resultant entanglement is established between telecom-wavelength photons at either end of the 50 km channel. Finally, the system improvements to allow for repeater-node chains to establish stored entanglement over 800 km at hertz rates are calculated, revealing a near-term path to distributed networks of entangled sensors, atomic clocks, and quantum processors.

Quantum Interference between Fundamentally Different Processes Is Enabled by Shaped Input Wavefunctions

This work presents a general framework for quantum interference between processes that can involve different fundamental particles or quasi-particles. This framework shows that shaping input wavefunctions is a versatile and powerful tool for producing and controlling quantum interference between distinguishable pathways, beyond previously explored quantum interference between indistinguishable pathways. Two examples of quantum interference enabled by shaping in interactions between free electrons, bound electrons, and photons are presented: i) the vanishing of the zero-loss peak by destructive quantum interference when a shaped electron wavepacket couples to light, under conditions where the electron's zero-loss peak otherwise dominates; ii) quantum interference between free electron and atomic (bound electron) spontaneous emission processes, which can be significant even when the free electron and atom are far apart, breaking the common notion that a free electron and an atom must be close by to significantly affect each other's processes. Conclusions show that emerging quantum wave-shaping techniques unlock the door to greater versatility in light-matter interactions and other quantum processes in general.

Entanglement of Trapped-Ion Qubits Separated by 230 Meters

We report on an elementary quantum network of two atomic ions separated by 230 m. The ions are trapped in different buildings and connected with 520(2) m of optical fiber. At each network node, the electronic state of an ion is entangled with the polarization state of a single cavity photon; subsequent to interference of the photons at a beam splitter, photon detection heralds entanglement between the two ions. Fidelities of up to (88.0+2.2-4.7)% are achieved with respect to a maximally entangled Bell state, with a success probability of 4×10^{-5}. We analyze the routes to improve these metrics, paving the way for long-distance networks of entangled quantum processors.

On the Fidelity Robustness of CHSH-Bell Inequality via Filtered Random States

The theorem developed by John Bell constituted the starting point of a revolution that translated a philosophical question about the nature of reality into the broad and intense field of research of the quantum information technologies. We focus on a system of two qubits prepared in a random, mixed state, and we study the typical behavior of their nonlocality via the CHSH-Bell inequality. Afterward, motivated by the necessity of accounting for inefficiency in the state preparation, we address to what extent states close enough to one with a high degree of nonclassicality can violate local realism with a previously chosen experimental setup.

Hong-Ou-Mandel Interference between Two Hyperentangled Photons Enables Observation of Symmetric and Antisymmetric Particle Exchange Phases

Two-photon Hong-Ou-Mandel (HOM) interference is a fundamental quantum effect with no classical counterpart. The existing research on two-photon interference was mainly limited in one degree of freedom (DOF); hence, it is still a challenge to realize quantum interference in multiple DOFs. Here, we demonstrate HOM interference between two hyperentangled photons in two DOFs of polarization and orbital angular momentum (OAM) for all 16 hyperentangled Bell states. We observe hyperentangled two-photon interference with a bunching effect for ten symmetric states (nine boson-boson states and one fermion-fermion state) and an antibunching effect for six antisymmetric states (three boson-fermion states and three fermion-boson states). More interestingly, expanding the Hilbert space by introducing an extra DOF for two photons enables one to transfer the unmeasurable external phase in the initial DOF to a measurable internal phase in the expanded two DOFs. We directly measured the symmetric exchange phases being 0.012±0.002, 0.025±0.002, and 0.027±0.002 in radian for the three boson states in OAM and the antisymmetric exchange phase being 0.991π±0.002 in radian for the other fermion state, as theoretical predictions. Our Letter may not only pave the way for more wide applications of quantum interference, but also develop new technologies by expanding Hilbert space in more DOFs.

On-Demand Storage of Photonic Qubits at Telecom Wavelengths

Quantum memories at telecom wavelengths are crucial for the construction of large-scale quantum networks based on existing fiber networks. On-demand storage of telecom photonic qubits is an essential request for such networking applications but yet to be demonstrated. Here we demonstrate the storage and on-demand retrieval of telecom photonic qubits using a laser-written waveguide fabricated in an ^{167}Er^{3+}:Y_{2}SiO_{5} crystal. Both ends of the waveguide memory are directly connected with fiber arrays with a fiber-to-fiber efficiency of 51%. Storage fidelity of 98.3(1)% can be obtained for time-bin qubits encoded with single-photon-level coherent pulses, which is far beyond the maximal fidelity that can be achieved with a classical measure and prepared strategy. This device features high reliability and easy scalability, and it can be directly integrated into fiber networks, which could play an essential role in fiber-based quantum networks.

High-Dimensional Bell Test without Detection Loophole

Violation of Bell's inequalities shows strong conflict between quantum mechanics and local realism. Loophole-free Bell tests not only deepen understanding of quantum mechanics, but are also important foundations for device-independent (DI) tasks in quantum information. High-dimensional quantum systems offer a significant advantage over qubits for closing the detection loophole. In the symmetric scenario, a detection efficiency as low as 61.8% can be tolerated using four-dimensional states and a four-setting Bell inequality [Phys. Rev. Lett. 104, 060401 (2010)PRLTAO0031-900710.1103/PhysRevLett.104.060401]. For the first time, we show that four-dimensional entangled photons violate a Bell inequality while closing the detection loophole in experiment. The detection efficiency of the four-dimensional entangled source is about 71.7%, and the fidelity of the state is 0.995±0.001. Combining the technique of multicore fibers, the realization of loophole-free high-dimensional Bell tests and high-dimensional quantum DI technologies are promising.

Postselected Entanglement between Two Atomic Ensembles Separated by 12.5 km

Quantum internet gives the promise of getting all quantum resources connected, and it will enable applications far beyond a localized scenario. A prototype is a network of quantum memories that are entangled and well separated. In this Letter, we report the establishment of postselected entanglement between two atomic quantum memories physically separated by 12.5 km directly. We create atom-photon entanglement in one node and send the photon to a second node for storage via electromagnetically induced transparency. We harness low-loss transmission through a field-deployed fiber of 20.5 km by making use of frequency down-conversion and up-conversion. The final memory-memory entanglement is verified to have a fidelity of 90% via retrieving to photons. Our experiment makes a significant step forward toward the realization of a practical metropolitan-scale quantum network.

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.

A device-independent quantum key distribution system for distant users

Device-independent quantum key distribution (DIQKD) enables the generation of secret keys over an untrusted channel using uncharacterized and potentially untrusted devices^1-9. The proper and secure functioning of the devices can be certified by a statistical test using a Bell inequality^10-12. This test originates from the foundations of quantum physics and also ensures robustness against implementation loopholes¹³, thereby leaving only the integrity of the users' locations to be guaranteed by other means. The realization of DIQKD, however, is extremely challenging-mainly because it is difficult to establish high-quality entangled states between two remote locations with high detection efficiency. Here we present an experimental system that enables for DIQKD between two distant users. The experiment is based on the generation and analysis of event-ready entanglement between two independently trapped single rubidium atoms located in buildings 400 metre apart¹⁴. By achieving an entanglement fidelity of [Formula: see text] and implementing a DIQKD protocol with random key basis¹⁵, we observe a significant violation of a Bell inequality of S = 2.578(75)-above the classical limit of 2-and a quantum bit error rate of only 0.078(9). For the protocol, this results in a secret key rate of 0.07 bits per entanglement generation event in the asymptotic limit, and thus demonstrates the system's capability to generate secret keys. Our results of secure key exchange with potentially untrusted devices pave the way to the ultimate form of quantum secure communications in future quantum networks.

Frequency Conversion Interface towards Quantum Network: From Atomic Transition Line to Fiber Optical Communication Band

Quantum repeater is a key component of quantum network, and atomic memory is one of the important candidates for constructing quantum repeater. However, the atomic transition wavelength is not suitable for long-distance transmission in optical fiber. To bridge atomic memory and fiber communication, we demonstrate a frequency conversion interface from rubidium D1 line (795 nm) to the optical communication L-band (1621 nm) based on difference frequency generation. To reduce broadband noise of spontaneous Raman scattering caused by strong pumping light, we use a combination of two cascaded etalons and a Fabry-Perot cavity with low finesse to narrow the noise bandwidth to 11.7 MHz. The filtering system is built by common optical elements and is easy to use; it can be widely applied in frequency conversion process. We show that the signal-noise ratio of the converted field is good enough to reduce the input photon number below 1 under the condition of low external device conversion efficiency (0.51%) and large duration of input pulse (250 ns). The demonstrated frequency conversion interface has important potential application in quantum networks.

A local area quantum teleportation network based on an array of electrically activated graphene waveguides

We present a scheme to generate a continuous variable (CV) multipartite entangled state using an array of plasmonic graphene waveguides that are activated by nonclassical driving microwave modes. Within this scheme, we can exploit the interaction of two light fields coupled to the same microwave mode in each waveguide to produce any type of multipartite Gaussian entangled state. A teleportation network is illustrated using the resultant CV multipartite entangled state. In particular, the proposed setup enables coherent state teleportation across remotely connected nodes with fidelity above a threshold limit of 2/3, providing secure quantum teleportation networking even in the presence of losses.

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.

Generation of entanglement between a highly wave-packet-tunable photon and a spin-wave memory in cold atoms

Controls of waveforms (pulse durations) of single photons are important tasks for effectively interconnecting disparate atomic memories in hybrid quantum networks. So far, the waveform control of a single photon that is entangled with an atomic memory remains unexplored. Here, we demonstrated control of waveform length of the photon that is entangled with an atomic spin-wave memory by varying light-atom interaction time in cold atoms. The Bell parameter S as a function of the duration of photon pulse is measured, which shows that violations of Bell inequality can be achieved for the photon pulse in the duration range from 40 ns to 50 µs, where, S = 2.64 ± 0.02 and S = 2.26 ± 0.05 for the 40-ns and 50-µs durations, respectively. The measured results show that S parameter decreases with the increase in the pulse duration. We confirm that the increase in photon noise probability per pulse with the pulse-duration is responsible for the S decrease.

Entanglement between a Telecom Photon and an On-Demand Multimode Solid-State Quantum Memory

Entanglement between photons at telecommunication wavelengths and long-lived quantum memories is one of the fundamental requirements of long-distance quantum communication. Quantum memories featuring on-demand readout and multimode operation are additional precious assets that will benefit the communication rate. In this Letter, we report the first demonstration of entanglement between a telecom photon and a collective spin excitation in a multimode solid-state quantum memory. Photon pairs are generated through widely nondegenerate parametric down-conversion, featuring energy-time entanglement between the telecom-wavelength idler and a visible signal photon. The latter is stored in a Pr^{3+}:Y_{2}SiO_{5} crystal as a spin wave using the full atomic frequency comb scheme. We then recall the stored signal photon and analyze the entanglement using the Franson scheme. We measure conditional fidelities of 92(2)% for excited-state storage, enough to violate a Clauser-Horne-Shimony-Holt inequality, and 77(2)% for spin-wave storage. Taking advantage of the on-demand readout from the spin state, we extend the entanglement storage in the quantum memory for up to 47.7  μs, which could allow for the distribution of entanglement between quantum nodes separated by distances of up to 10 km.

Relativistic Bell Test within Quantum Reference Frames

A still widely debated question in the field of relativistic quantum information is whether entanglement and the degree of violation of Bell's inequalities for massive relativistic particles are frame independent or not. At the core of this question is the effect that spin gets entangled with the momentum degree of freedom at relativistic velocities. Here, we show that Bell's inequalities for a pair of particles can be maximally violated in a special-relativistic regime, even without any postselection of the momentum of the particles. To this end, we use the methodology of quantum reference frames, which allows us to transform the problem to the rest frame of a particle, whose state can be in a superposition of relativistic momenta from the viewpoint of the laboratory frame. We show that, when the relative motion of two particles is noncollinear, the optimal measurements for violation of Bell's inequalities in the laboratory frame involve "coherent Wigner rotations." Moreover, the degree of violation of Bell's inequalities is independent of the choice of the quantum reference frame. Our results open up the possibility of extending entanglement-based quantum communication protocols to relativistic regimes.

Telecom-heralded entanglement between multimode solid-state quantum memories

Future quantum networks will enable the distribution of entanglement between distant locations and allow applications in quantum communication, quantum sensing and distributed quantum computation¹. At the core of this network lies the ability to generate and store entanglement at remote, interconnected quantum nodes². Although various remote physical systems have been successfully entangled^3-12, none of these realizations encompassed all of the requirements for network operation, such as compatibility with telecommunication (telecom) wavelengths and multimode operation. Here we report the demonstration of heralded entanglement between two spatially separated quantum nodes, where the entanglement is stored in multimode solid-state quantum memories. At each node a praseodymium-doped crystal^13,14 stores a photon of a correlated pair¹⁵, with the second photon at telecom wavelengths. Entanglement between quantum memories placed in different laboratories is heralded by the detection of a telecom photon at a rate up to 1.4 kilohertz, and the entanglement is stored in the crystals for a pre-determined storage time up to 25 microseconds. We also show that the generated entanglement is robust against loss in the heralding path, and demonstrate temporally multiplexed operation, with 62 temporal modes. Our realization is extendable to entanglement over longer distances and provides a viable route towards field-deployed, multiplexed quantum repeaters based on solid-state resources.

Heralded entanglement distribution between two absorptive quantum memories

Owing to the inevitable loss in communication channels, the distance of entanglement distribution is limited to approximately 100 kilometres on the ground¹. Quantum repeaters can circumvent this problem by using quantum memory and entanglement swapping². As the elementary link of a quantum repeater, the heralded distribution of two-party entanglement between two remote nodes has only been realized with built-in-type quantum memories^3-9. These schemes suffer from the trade-off between multiplexing capacity and deterministic properties and hence hinder the development of efficient quantum repeaters. Quantum repeaters based on absorptive quantum memories can overcome such limitations because they separate the quantum memories and the quantum light sources. Here we present an experimental demonstration of heralded entanglement between absorptive quantum memories. We build two nodes separated by 3.5 metres, each containing a polarization-entangled photon-pair source and a solid-state quantum memory with bandwidth up to 1 gigahertz. A joint Bell-state measurement in the middle station heralds the successful distribution of maximally entangled states between the two quantum memories with a fidelity of 80.4 ± 2.2 per cent (±1 standard deviation). The quantum nodes and channels demonstrated here can serve as an elementary link of a quantum repeater. Moreover, the wideband absorptive quantum memories used in the nodes are compatible with deterministic entanglement sources and can simultaneously support multiplexing, which paves the way for the construction of practical solid-state quantum repeaters and high-speed quantum networks.

Imaging Trapped Ion Structures via Fluorescence Cross-Correlation Detection

Cross-correlation signals are recorded from fluorescence photons scattered in free space off a trapped ion structure. The analysis of the signal allows for unambiguously revealing the spatial frequency, thus the distance, as well as the spatial alignment of the ions. For the case of two ions we obtain from the cross-correlations a spatial frequency f_{spatial}=1490±2_{stat}±8_{syst}  rad^{-1}, where the statistical uncertainty improves with the integrated number of correlation events as N^{-0.51±0.06}. We independently determine the spatial frequency to be 1494±11  rad^{-1}, proving excellent agreement. Expanding our method to the case of three ions, we demonstrate its functionality for two-dimensional arrays of emitters of indistinguishable photons, serving as a model system to yield structural information where direct imaging techniques fail.

Realization of a multinode quantum network of remote solid-state qubits

The distribution of entangled states across the nodes of a future quantum internet will unlock fundamentally new technologies. Here, we report on the realization of a three-node entanglement-based quantum network. We combine remote quantum nodes based on diamond communication qubits into a scalable phase-stabilized architecture, supplemented with a robust memory qubit and local quantum logic. In addition, we achieve real-time communication and feed-forward gate operations across the network. We demonstrate two quantum network protocols without postselection: the distribution of genuine multipartite entangled states across the three nodes and entanglement swapping through an intermediary node. Our work establishes a key platform for exploring, testing, and developing multinode quantum network protocols and a quantum network control stack.

Overcoming the rate-distance limit of device-independent quantum key distribution

Device-independent quantum key distribution (DIQKD) exploits the violation of a Bell inequality to extract secure keys even if users' devices are untrusted. Currently, all DIQKD protocols suffer from the secret key capacity bound, i.e., the secret key rate scales linearly with the transmittance of two users. Here we propose a heralded DIQKD scheme based on entangled coherent states to improve entangling rates whereby long-distance entanglement is created by single-photon-type interference. The secret key rate of our scheme can significantly outperform the traditional two-photon-type Bell-state measurement scheme and, importantly, surpass the above capacity bound. Our protocol therefore is an important step towards a realization of DIQKD and can be a promising candidate scheme for entanglement swapping in the future quantum internet.

Bell inequalities for entangled qubits: quantitative tests of quantum character and nonlocality on quantum computers

This work provides quantitative tests of the extent of violation of two inequalities applicable to qubits coupled into Bell states, using IBM's publicly accessible quantum computers. Violations of the inequalities are well established. Our purpose is not to test the inequalities, but rather to determine how well quantum mechanical predictions can be reproduced on quantum computers, given their current fault rates. We present results for the spin projections of two entangled qubits, along three axes A, B, and C, with a fixed angle θ between A and B and a range of angles θ' between B and C. For any classical object that can be characterized by three observables with two possible values, inequalities govern relationships among the probabilities of outcomes for the observables, taken pairwise. From set theory, these inequalities must be satisfied by all such classical objects; but quantum systems may violate the inequalities. We have detected clear-cut violations of one inequality in runs on IBM's publicly accessible quantum computers. The Clauser-Horne-Shimony-Holt (CHSH) inequality governs a linear combination S of expectation values of products of spin projections, taken pairwise. Finding S > 2 rules out local, hidden variable theories for entangled quantum systems. We obtained values of S greater than 2 in our runs prior to error mitigation. To reduce the quantitative errors, we used a modification of the error-mitigation procedure in the IBM documentation. We prepared a pair of qubits in the state |00〉, found the probabilities to observe the states |00〉, |01〉, |10〉, and |11〉 in multiple runs, and used that information to construct the first column of an error matrix M. We repeated this procedure for states prepared as |01〉, |10〉, and |11〉 to construct the full matrix M, whose inverse is the filtering matrix. After applying filtering matrices to our averaged outcomes, we have found good quantitative agreement between the quantum computer output and the quantum mechanical predictions for the extent of violation of both inequalities as functions of θ'.

Two-photon interference: the Hong-Ou-Mandel effect

Nearly 30 years ago, two-photon interference was observed, marking the beginning of a new quantum era. Indeed, two-photon interference has no classical analogue, giving it a distinct advantage for a range of applications. The peculiarities of quantum physics may now be used to our advantage to outperform classical computations, securely communicate information, simulate highly complex physical systems and increase the sensitivity of precise measurements. This separation from classical to quantum physics has motivated physicists to study two-particle interference for both fermionic and bosonic quantum objects. So far, two-particle interference has been observed with massive particles, among others, such as electrons and atoms, in addition to plasmons, demonstrating the extent of this effect to larger and more complex quantum systems. A wide array of novel applications to this quantum effect is to be expected in the future. This review will thus cover the progress and applications of two-photon (two-particle) interference over the last three decades.

Microwave Quantum Link between Superconducting Circuits Housed in Spatially Separated Cryogenic Systems

Superconducting circuits are a strong contender for realizing quantum computing systems and are also successfully used to study quantum optics and hybrid quantum systems. However, their cryogenic operation temperatures and the current lack of coherence-preserving microwave-to-optical conversion solutions have hindered the realization of superconducting quantum networks spanning different cryogenic systems or larger distances. Here, we report the successful operation of a cryogenic waveguide coherently linking transmon qubits located in two dilution refrigerators separated by a physical distance of five meters. We transfer qubit states and generate entanglement on demand with average transfer and target state fidelities of 85.8% and 79.5%, respectively, between the two nodes of this elementary network. Cryogenic microwave links provide an opportunity to scale up systems for quantum computing and create local area superconducting quantum communication networks over length scales of at least tens of meters.

Bell correlations between light and vibration at ambient conditions

Time-resolved Raman spectroscopy techniques offer various ways to study the dynamics of molecular vibrations in liquids or gases and optical phonons in crystals. While these techniques give access to the coherence time of the vibrational modes, they are not able to reveal the fragile quantum correlations that are spontaneously created between light and vibration during the Raman interaction. Here, we present a scheme leveraging universal properties of spontaneous Raman scattering to demonstrate Bell correlations between light and a collective molecular vibration. We measure the decay of these hybrid photon-phonon Bell correlations with sub-picosecond time resolution and find that they survive over several hundred oscillations at ambient conditions. Our method offers a universal approach to generate entanglement between light and molecular vibrations. Moreover, our results pave the way for the study of quantum correlations in more complex solid-state and molecular systems in their natural state.

Phase Matching in Lower Dimensions

Phase matching refers to a process in which atom-field interactions lead to the creation of an output field that propagates coherently through the interaction volume. By studying light scattering from arrays of cold atoms, we show that conditions for phase matching change as the dimensionality of the system decreases. In particular, for a single atomic chain, there is phase-matched reflective scattering in a cone about the symmetry axis of the array that scales as the square of the number of atoms in the chain. For two chains of atoms, the phase-matched reflective scattering can be enhanced or diminished as a result of Bragg scattering. Such scattering can be used for mapping collective states within an array of neutral atoms onto propagating light fields and for establishing quantum links between separated arrays.

Two-way single-photon-level frequency conversion between 852 nm and 1560 nm for connecting cesium D2 line with the telecom C-band

A compact setup for two-way single-photon-level frequency conversion between 852 nm and 1560 nm has been implemented with the same periodically-poled magnesium-oxide-doped lithium niobate (PPMgO:LN) bulk crystals for connecting cesium D2 line (852 nm) to telecom C-band. By single-pass mixing a strong continuous-wave pump laser at 1878 nm and the single-photon-level periodical signal pulses in a 50-mm-long PPMgO:LN bulk crystal, the conversion efficiency of ∼ 1.7% (∼ 1.9%) for 852-nm to 1560-nm down-conversion (1560-nm to 852-nm up-conversion) have been achieved. We analyzed noise photons induced by the strong pump laser beam, including the spontaneous Raman scattering (SRS) and the spontaneous parametric down-conversion (SPDC) photons, and the photons generated in the cascaded nonlinear processes. The signal-to-noise ratio (SNR) has been improved remarkably by using the narrow-band filters and changing polarization of the noise photons in the difference frequency generation (DFG) process. With further improvement of the conversion efficiency by employing PPMgO:LN waveguide, instead of bulk crystal, our study may provide the basics for cyclic photon conversion in quantum network.

Bright-light detector control emulates the local bounds of Bell-type inequalities

It is well-known that no local model-in theory-can simulate the outcome statistics of a Bell-type experiment as long as the detection efficiency is higher than a threshold value. For the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality this theoretical threshold value is [Formula: see text]. On the other hand, Phys. Rev. Lett. 107, 170404 (2011) outlined an explicit practical model that can fake the CHSH inequality for a detection efficiency of up to 0.5. In this work, we close this gap. More specifically, we propose a method to emulate a Bell inequality at the threshold detection efficiency using existing optical detector control techniques. For a Clauser-Horne-Shimony-Holt inequality, it emulates the CHSH violation predicted by quantum mechanics up to [Formula: see text]. For the Garg-Mermin inequality-re-calibrated by incorporating non-detection events-our method emulates its exact local bound at any efficiency above the threshold. This confirms that attacks on secure quantum communication protocols based on Bell violation is a real threat if the detection efficiency loophole is not closed.

Light-mediated strong coupling between a mechanical oscillator and atomic spins 1 meter apart

Engineering strong interactions between quantum systems is essential for many phenomena of quantum physics and technology. Typically, strong coupling relies on short-range forces or on placing the systems in high-quality electromagnetic resonators, which restricts the range of the coupling to small distances. We used a free-space laser beam to strongly couple a collective atomic spin and a micromechanical membrane over a distance of 1 meter in a room-temperature environment. The coupling is highly tunable and allows the observation of normal-mode splitting, coherent energy exchange oscillations, two-mode thermal noise squeezing, and dissipative coupling. Our approach to engineering coherent long-distance interactions with light makes it possible to couple very different systems in a modular way, opening up a range of opportunities for quantum control and coherent feedback networks.

Light of Two Atoms in Free Space: Bunching or Antibunching?

Photon statistics divides light sources into three different categories, characterized by bunched, antibunched, or uncorrelated photon arrival times. Single atoms, ions, molecules, or solid state emitters display antibunching of photons, while classical thermal sources exhibit photon bunching. Here we demonstrate a light source in free space, where the photon statistics depends on the direction of observation, undergoing a continuous crossover between photon bunching and antibunching. We employ two trapped ions, observe their fluorescence under continuous laser light excitation, and record spatially resolved the autocorrelation function g^{(2)}(τ) with a movable Hanbury Brown and Twiss detector. Varying the detector position we find a minimum value for antibunching, g^{(2)}(0)=0.60(5) and a maximum of g^{(2)}(0)=1.46(8) for bunching, demonstrating that this source radiates fundamentally different types of light alike. The observed variation of the autocorrelation function is understood in the Dicke model from which the observed maximum and minimum values can be modeled, taking independently measured experimental parameters into account.

Entanglement of two quantum memories via fibres over dozens of kilometres

A quantum internet that connects remote quantum processors^1,2 should enable a number of revolutionary applications such as distributed quantum computing. Its realization will rely on entanglement of remote quantum memories over long distances. Despite enormous progress^3-12, at present the maximal physical separation achieved between two nodes is 1.3 kilometres¹⁰, and challenges for longer distances remain. Here we demonstrate entanglement of two atomic ensembles in one laboratory via photon transmission through city-scale optical fibres. The atomic ensembles function as quantum memories that store quantum states. We use cavity enhancement to efficiently create atom-photon entanglement^13-15 and we use quantum frequency conversion¹⁶ to shift the atomic wavelength to telecommunications wavelengths. We realize entanglement over 22 kilometres of field-deployed fibres via two-photon interference^17,18 and entanglement over 50 kilometres of coiled fibres via single-photon interference¹⁹. Our experiment could be extended to nodes physically separated by similar distances, which would thus form a functional segment of the atomic quantum network, paving the way towards establishing atomic entanglement over many nodes and over much longer distances.

Long-Distance Distribution of Atom-Photon Entanglement at Telecom Wavelength

Entanglement between stationary quantum memories and photonic channels is the essential resource for future quantum networks. Together with entanglement distillation, it will enable efficient distribution of quantum states. We report on the generation and observation of entanglement between a ^{87}Rb atom and a photon at telecom wavelength transmitted through up to 20 km of optical fiber. For this purpose, we use polarization-preserving quantum frequency conversion to transform the wavelength of a photon entangled with the atomic spin state from 780 nm to the telecom S band at 1522 nm. We achieve an unprecedented external device conversion efficiency of 57% and observe an entanglement fidelity between the atom and telecom photon of ≥78.5±0.9% after transmission through 20 km of optical fiber, mainly limited by decoherence of the atomic state. This result is an important milestone on the road to distribute quantum information on a large scale.

Proposal for Heralded Generation and Detection of Entangled Microwave-Optical-Photon Pairs

Quantum state transfer between microwave and optical frequencies is essential for connecting superconducting quantum circuits to optical systems and extending microwave quantum networks over long distances. However, establishing such a quantum interface is extremely challenging because the standard direct quantum transduction requires both high coupling efficiency and small added noise. We propose an entanglement-based scheme-generating microwave-optical entanglement and using it to transfer quantum states via quantum teleportation-which can bypass the stringent requirements in direct quantum transduction and is robust against loss errors. In addition, we propose and analyze a counterintuitive design-suppress the added noise by placing the device at a higher temperature environment-which can improve both the device quality factor and power handling capability. We systematically analyze the generation and verification of entangled microwave-optical-photon pairs. The parameter for entanglement verification favors the regime of cooperativity mismatch and can tolerate certain thermal noises. Our scheme is feasible given the latest advances on electro-optomechanics, and can be generalized to various physical systems.

Measurement Induced Synthesis of Coherent Quantum Batteries

Quantum coherence represented by a superposition of energy eigenstates is, together with energy, an important resource for quantum technology and thermodynamics. Energy and quantum coherence however, can be complementary. The increase of energy can reduce quantum coherence and vice versa. Recently, it was realized that steady-state quantum coherence could be autonomously harnessed from a cold environment. We propose a conditional synthesis of N independent two-level systems (TLS) with partial quantum coherence obtained from an environment to one coherent system using a measurement able to increase both energy and coherence simultaneously. The measurement process acts here as a Maxwell demon synthesizing the coherent energy of individual TLS to one large coherent quantum battery. The measurement process described by POVM elements is diagonal in energy representation and, therefore, it does not project on states with quantum coherence at all. We discuss various strategies and their efficiency to reach large coherent energy of the battery. After numerical optimization and proof-of-principle tests, it opens way to feasible repeat-until-success synthesis of coherent quantum batteries from steady-state autonomous coherence.

Field dynamics in atrioventricular activation. Clinical evidence of a specific field-to-protein interaction

The atrioventricular node (AV) is considered the electrical connection between the atria and ventricles. There is an electrical pause between activation of the atria and the ventricles (PR segment), but to date the mechanism responsible for this interruption remains unclear. The present communication focuses on the hypothesis that magnetic field dynamics could provide the answer. Proof of this hypothesis is that in Wolff-Parkinson-White syndrome, where there is physical connection between the atria and ventricles (bundle of Kent), there is electrical AV continuity, no PR segment is detected, and catheter ablation of the abnormal bundle restores AV discontinuity. Spontaneous initiation of the heart at the level of the sinus node, the pacemaker of the heart, could also be explained via field dynamics. The known transmembrane pacemaker protein CHN4, present in both sinoatrial and AV nodal cells, could interact with field information to provide specificity in an electronic key-to-lock mechanism interaction.

Neo-Naturalism, Conciliatory Explanations, and Spatiotemporal Surprises

Some materialists believe that physics is rich enough to bridge Levine's Explanatory Gap, while others believe that it is not. Here I promote an intermediate position holding that physics is rich enough to explain why this gap seems more intractable than similar inter-theoretic explanatory gaps, without providing a full-blown "physical" explanation of consciousness. At a minimum, such an approach needs to explore the prospects of empirical discoveries that can diminish the power of anti-physicalist arguments like Chalmers's "conceivability argument" and Jackson's "knowledge argument." While this is not an easy task, recent advances in the physics of spacetime and information convince us that these prospects are not poor. The empirical bent of this approach suggests framing it as a naturalist theory of mind seeking to situate or make room for consciousness within our great naturalist system, but the reliance of this approach on recent (re)conceptions of time and information pulls the carpet out from under essential concepts like concreteness and causation, thus demanding a radically reconfigured naturalism, or neo-naturalism. The question that will frame this discussion is, "What could possibly count as an empirical fact that can help naturalize consciousness?"

Quantum internet: A vision for the road ahead

The internet—a vast network that enables simultaneous long-range classical communication—has had a revolutionary impact on our world. The vision of a quantum internet is to fundamentally enhance internet technology by enabling quantum communication between any two points on Earth. Such a quantum internet may operate in parallel to the internet that we have today and connect quantum processors in order to achieve capabilities that are provably impossible by using only classical means. Here, we propose stages of development toward a full-blown quantum internet and highlight experimental and theoretical progress needed to attain them.

Test of Local Realism into the Past without Detection and Locality Loopholes

Inspired by the recent remarkable progress in the experimental test of local realism, we report here such a test that achieves an efficiency greater than (78%)^{2} for entangled photon pairs separated by 183 m. Further utilizing the randomness in cosmic photons from pairs of stars on the opposite sides of the sky for the measurement setting choices, we not only close the locality and detection loopholes simultaneously, but also test the null hypothesis against local hidden variable mechanisms for events that took place 11 years ago (13 orders of magnitude longer than previous experiments). After considering the bias in measurement setting choices, we obtain an upper bound on the p value of 7.87×10^{-4}, which clearly indicates the rejection with high confidence of potential local hidden variable models. One may further push the time constraint on local hidden variable mechanisms deep into the cosmic history by taking advantage of the randomness in photon emissions from quasars with large aperture telescopes.

Generation of multiqubit steady-state quantum correlation by squeezed-reservoir engineering

Stationary quantum correlation among two-level systems (TLSs) in steady state is one of unique resources for applications in quantum information processing. Here we propose a scheme to generate such quantum correlation among the TLSs inside a lossy cavity. It is found that, by applying a broadband squeezed laser acting as a squeezed-vacuum reservoir to the cavity, a stable quantum correlation of the TLSs can be generated. By adiabatically eliminating the cavity field, we derive a reduced master equation of the TLSs in the bad-cavity limit. We show that the generated quantum correlation is essentially determined by the squeezing features transferred from the squeezed-vacuum reservoir via the cavity field as a quantum bus. We study the effect of the system parameters, such as the squeezing, the detuning, the coupling strength, and the decay rate of the TLSs, on the performance of the scheme. The feasibility of our proposal is supported by the application of currently available experimental techniques.

Frequency-domain Hong-Ou-Mandel interference with linear optics

The Hong-Ou-Mandel (HOM) interference is one of the most fundamental quantum-mechanical effects that reveal a nonclassical behavior of single photons. Two identical photons that are incident on the input ports of an unbiased beam splitter always exit the beam splitter together from the same output port, an effect referred to as photon bunching. In this Letter, we utilize a single electro-optic phase modulator as a probabilistic frequency beam splitter, which we exploit to observe HOM interference between two photons that are in different spectral modes, yet are identical in other characteristics. Our approach enables linear optical quantum information processing protocols using the frequency degree of freedom in photons such as quantum computing techniques with linear optics.

Machine Learning Detection of Bell Nonlocality in Quantum Many-Body Systems

Machine learning, the core of artificial intelligence and big data science, is one of today's most rapidly growing interdisciplinary fields. Recently, machine learning tools and techniques have been adopted to tackle intricate quantum many-body problems. In this Letter, we introduce machine learning techniques to the detection of quantum nonlocality in many-body systems, with a focus on the restricted-Boltzmann-machine (RBM) architecture. Using reinforcement learning, we demonstrate that RBM is capable of finding the maximum quantum violations of multipartite Bell inequalities with given measurement settings. Our results build a novel bridge between computer-science-based machine learning and quantum many-body nonlocality, which will benefit future studies in both areas.