Quantum teleportation of physical qubits into logical code spaces.

Quantum error correction is an essential tool for reliably performing tasks for processing quantum information on a large scale. However, integration into quantum circuits to achieve these tasks is problematic when one realizes that nontransverse operations, which are essential for universal quantum computation, lead to the spread of errors. Quantum gate teleportation has been proposed as an elegant solution for this. Here, one replaces these fragile, nontransverse inline gates with the generation of specific, highly entangled offline resource states that can be teleported into the circuit to implement the nontransverse gate. As the first important step, we create a maximally entangled state between a physical and an error-correctable logical qubit and use it as a teleportation resource. We then demonstrate the teleportation of quantum information encoded on the physical qubit into the error-corrected logical qubit with fidelities up to 0.786. Our scheme can be designed to be fully fault tolerant so that it can be used in future large-scale quantum technologies.

One-Photon Measurement of Two-Photon Entanglement.

Measuring entanglement is an essential step in a wide range of applied and foundational quantum experiments. When a two-particle quantum state is not pure, standard methods to measure the entanglement require detection of both particles. We realize a conceptually new method for verifying and measuring entanglement in a class of two-part (bipartite) mixed states. Contrary to the approaches known to date, in our experiment we verify and measure entanglement in mixed quantum bipartite states by detecting only one subsystem, the other remains undetected. Only one copy of the mixed or pure state is used but that state is in a superposition of having been created in two identical sources. We show that information shared in entangled systems can be accessed through single-particle interference patterns. Our experiment enables entanglement characterization even when one of the subsystems cannot be detected, for example, when suitable detectors are not available.

Predicting research trends with semantic and neural networks with an application in quantum physics.

The vast and growing number of publications in all disciplines of science cannot be comprehended by a single human researcher. As a consequence, researchers have to specialize in narrow subdisciplines, which makes it challenging to uncover scientific connections beyond the own field of research. Thus, access to structured knowledge from a large corpus of publications could help push the frontiers of science. Here, we demonstrate a method to build a semantic network from published scientific literature, which we call SemNet We use SemNet to predict future trends in research and to inspire personalized and surprising seeds of ideas in science. We apply it in the discipline of quantum physics, which has seen an unprecedented growth of activity in recent years. In SemNet, scientific knowledge is represented as an evolving network using the content of 750,000 scientific papers published since 1919. The nodes of the network correspond to physical concepts, and links between two nodes are drawn when two concepts are concurrently studied in research articles. We identify influential and prize-winning research topics from the past inside SemNet, thus confirming that it stores useful semantic knowledge. We train a neural network using states of SemNet of the past to predict future developments in quantum physics and confirm high-quality predictions using historic data. Using network theoretical tools, we can suggest personalized, out-of-the-box ideas by identifying pairs of concepts, which have unique and extremal semantic network properties. Finally, we consider possible future developments and implications of our findings.

Path identity as a source of high-dimensional entanglement.

We present an experimental demonstration of a general entanglement-generation framework, where the form of the entangled state is independent of the physical process used to produce the particles. It is the indistinguishability of multiple generation processes and the geometry of the setup that give rise to the entanglement. Such a framework, termed entanglement by path identity, exhibits a high degree of customizability. We employ one class of such geometries to build a modular source of photon pairs that are high-dimensionally entangled in their orbital angular momentum. We demonstrate the creation of three-dimensionally entangled states and show how to incrementally increase the dimensionality of entanglement. The generated states retain their quality even in higher dimensions. In addition, the design of our source allows for its generalization to various degrees of freedom and even for the implementation in integrated compact devices. The concept of entanglement by path identity itself is a general scheme and allows for construction of sources producing also customized states of multiple photons. We therefore expect that future quantum technologies and fundamental tests of nature in higher dimensions will benefit from this approach.

Quantum experiments and graphs II: Quantum interference, computation, and state generation.

We present an approach to describe state-of-the-art photonic quantum experiments using graph theory. There, the quantum states are given by the coherent superpositions of perfect matchings. The crucial observation is that introducing complex weights in graphs naturally leads to quantum interference. This viewpoint immediately leads to many interesting results, some of which we present here. First, we identify an experimental unexplored multiphoton interference phenomenon. Second, we find that computing the results of such experiments is #P-hard, which means it is a classically intractable problem dealing with the computation of a matrix function Permanent and its generalization Hafnian. Third, we explain how a recent no-go result applies generally to linear optical quantum experiments, thus revealing important insights into quantum state generation with current photonic technology. Fourth, we show how to describe quantum protocols such as entanglement swapping in a graphical way. The uncovered bridge between quantum experiments and graph theory offers another perspective on a widely used technology and immediately raises many follow-up questions.

Entanglement distribution over a 96-km-long submarine optical fiber.

Quantum entanglement is one of the most extraordinary effects in quantum physics, with many applications in the emerging field of quantum information science. In particular, it provides the foundation for quantum key distribution (QKD), which promises a conceptual leap in information security. Entanglement-based QKD holds great promise for future applications owing to the possibility of device-independent security and the potential of establishing global-scale quantum repeater networks. While other approaches to QKD have already reached the level of maturity required for operation in absence of typical laboratory infrastructure, comparable field demonstrations of entanglement-based QKD have not been performed so far. Here, we report on the successful distribution of polarization-entangled photon pairs between Malta and Sicily over 96 km of submarine optical telecommunications fiber. We observe around 257 photon pairs per second, with a polarization visibility above 90%. Our results show that QKD based on polarization entanglement is now indeed viable in long-distance fiber links. This field demonstration marks the longest-distance distribution of entanglement in a deployed telecommunications network and demonstrates an international submarine quantum communication channel. This opens up myriad possibilities for future experiments and technological applications using existing infrastructure.

Active learning machine learns to create new quantum experiments.

How useful can machine learning be in a quantum laboratory? Here we raise the question of the potential of intelligent machines in the context of scientific research. A major motivation for the present work is the unknown reachability of various entanglement classes in quantum experiments. We investigate this question by using the projective simulation model, a physics-oriented approach to artificial intelligence. In our approach, the projective simulation system is challenged to design complex photonic quantum experiments that produce high-dimensional entangled multiphoton states, which are of high interest in modern quantum experiments. The artificial intelligence system learns to create a variety of entangled states and improves the efficiency of their realization. In the process, the system autonomously (re)discovers experimental techniques which are only now becoming standard in modern quantum optical experiments-a trait which was not explicitly demanded from the system but emerged through the process of learning. Such features highlight the possibility that machines could have a significantly more creative role in future research.

Computer-Inspired Concept for High-Dimensional Multipartite Quantum Gates.

An open question in quantum optics is how to manipulate and control complex quantum states in an experimentally feasible way. Here we present concepts for transformations of high-dimensional multiphotonic quantum systems. The proposals rely on two new ideas: (i) a novel high-dimensional quantum nondemolition measurement, (ii) the encoding and decoding of the entire quantum transformation in an ancillary state for sharing the necessary quantum information between the involved parties. Many solutions can readily be performed in laboratories around the world and thereby we identify important pathways for experimental research in the near future. The concepts have been found using the computer algorithm melvin for designing computer-inspired quantum experiments. As opposed to the field of machine learning, here the human learns new scientific concepts by interpreting and analyzing the results presented by the machine. This demonstrates that computer algorithms can inspire new ideas in science, which has a widely unexplored potential that goes far beyond experimental quantum information science.

Quantum imaging with undetected photons.

Information is central to quantum mechanics. In particular, quantum interference occurs only if there exists no information to distinguish between the superposed states. The mere possibility of obtaining information that could distinguish between overlapping states inhibits quantum interference. Here we introduce and experimentally demonstrate a quantum imaging concept based on induced coherence without induced emission. Our experiment uses two separate down-conversion nonlinear crystals (numbered NL1 and NL2), each illuminated by the same pump laser, creating one pair of photons (denoted idler and signal). If the photon pair is created in NL1, one photon (the idler) passes through the object to be imaged and is overlapped with the idler amplitude created in NL2, its source thus being undefined. Interference of the signal amplitudes coming from the two crystals then reveals the image of the object. The photons that pass through the imaged object (idler photons from NL1) are never detected, while we obtain images exclusively with the signal photons (from NL1 and NL2), which do not interact with the object. Our experiment is fundamentally different from previous quantum imaging techniques, such as interaction-free imaging or ghost imaging, because now the photons used to illuminate the object do not have to be detected at all and no coincidence detection is necessary. This enables the probe wavelength to be chosen in a range for which suitable detectors are not available. To illustrate this, we show images of objects that are either opaque or invisible to the detected photons. Our experiment is a prototype in quantum information--knowledge can be extracted by, and about, a photon that is never detected.

Quantifying the momentum correlation between two light beams by detecting one.

We report a measurement of the transverse momentum correlation between two photons by detecting only one of them. Our method uses two identical sources in an arrangement in which the phenomenon of induced coherence without induced emission is observed. In this way, we produce an interference pattern in the superposition of one beam from each source. We quantify the transverse momentum correlation by analyzing the visibility of this pattern. Our approach might be useful for the characterization of correlated photon pair sources and may lead to an experimental measure of continuous variable entanglement, which relies on the detection of only one of two entangled particles.

Quantum Teleportation in High Dimensions.

Quantum teleportation allows a "disembodied" transmission of unknown quantum states between distant quantum systems. Yet, all teleportation experiments to date were limited to a two-dimensional subspace of quantized multiple levels of the quantum systems. Here, we propose a scheme for teleportation of arbitrarily high-dimensional photonic quantum states and demonstrate an example of teleporting a qutrit. Measurements over a complete set of 12 qutrit states in mutually unbiased bases yield a teleportation fidelity of 0.75(1), which is well above both the optimal single-copy qutrit state-estimation limit of 1/2 and maximal qubit-qutrit overlap of 2/3, thus confirming a genuine and nonclassical three-dimensional teleportation. Our work will enable advanced quantum technologies in high dimensions, since teleportation plays a central role in quantum repeaters and quantum networks.

Bell violation using entangled photons without the fair-sampling assumption.

The violation of a Bell inequality is an experimental observation that forces the abandonment of a local realistic viewpoint--namely, one in which physical properties are (probabilistically) defined before and independently of measurement, and in which no physical influence can propagate faster than the speed of light. All such experimental violations require additional assumptions depending on their specific construction, making them vulnerable to so-called loopholes. Here we use entangled photons to violate a Bell inequality while closing the fair-sampling loophole, that is, without assuming that the sample of measured photons accurately represents the entire ensemble. To do this, we use the Eberhard form of Bell's inequality, which is not vulnerable to the fair-sampling assumption and which allows a lower collection efficiency than other forms. Technical improvements of the photon source and high-efficiency transition-edge sensors were crucial for achieving a sufficiently high collection efficiency. Our experiment makes the photon the first physical system for which each of the main loopholes has been closed, albeit in different experiments.

Quantum entanglement of angular momentum states with quantum numbers up to 10,010.

Photons with a twisted phase front carry a quantized amount of orbital angular momentum (OAM) and have become important in various fields of optics, such as quantum and classical information science or optical tweezers. Because no upper limit on the OAM content per photon is known, they are also interesting systems to experimentally challenge quantum mechanical prediction for high quantum numbers. Here, we take advantage of a recently developed technique to imprint unprecedented high values of OAM, namely spiral phase mirrors, to generate photons with more than 10,000 quanta of OAM. Moreover, we demonstrate quantum entanglement between these large OAM quanta of one photon and the polarization of its partner photon. To our knowledge, this corresponds to entanglement with the largest quantum number that has been demonstrated in an experiment. The results may also open novel ways to couple single photons to massive objects, enhance angular resolution, and highlight OAM as a promising way to increase the information capacity of a single photon.

Twisted light transmission over 143 km.

Spatial modes of light can potentially carry a vast amount of information, making them promising candidates for both classical and quantum communication. However, the distribution of such modes over large distances remains difficult. Intermodal coupling complicates their use with common fibers, whereas free-space transmission is thought to be strongly influenced by atmospheric turbulence. Here, we show the transmission of orbital angular momentum modes of light over a distance of 143 km between two Canary Islands, which is 50× greater than the maximum distance achieved previously. As a demonstration of the transmission quality, we use superpositions of these modes to encode a short message. At the receiver, an artificial neural network is used for distinguishing between the different twisted light superpositions. The algorithm is able to identify different mode superpositions with an accuracy of more than 80% up to the third mode order and decode the transmitted message with an error rate of 8.33%. Using our data, we estimate that the distribution of orbital angular momentum entanglement over more than 100 km of free space is feasible. Moreover, the quality of our free-space link can be further improved by the use of state-of-the-art adaptive optics systems.

Gouy Phase Radial Mode Sorter for Light: Concepts and Experiments.

We present an in principle lossless sorter for radial modes of light, using accumulated Gouy phases. The experimental setups have been found by a computer algorithm, and can be intuitively understood in a geometric way. Together with the ability to sort angular-momentum modes, we now have access to the complete two-dimensional transverse plane of light. The device can readily be used in multiplexing classical information. On a quantum level, it is an analog of the Stern-Gerlach experiment-significant for the discussion of fundamental concepts in quantum physics. As such, it can be applied in high-dimensional and multiphotonic quantum experiments.

Cosmic Bell Test Using Random Measurement Settings from High-Redshift Quasars.

In this Letter, we present a cosmic Bell experiment with polarization-entangled photons, in which measurement settings were determined based on real-time measurements of the wavelength of photons from high-redshift quasars, whose light was emitted billions of years ago; the experiment simultaneously ensures locality. Assuming fair sampling for all detected photons and that the wavelength of the quasar photons had not been selectively altered or previewed between emission and detection, we observe statistically significant violation of Bell's inequality by 9.3 standard deviations, corresponding to an estimated p value of ≲7.4×10^{-21}. This experiment pushes back to at least ∼7.8 Gyr ago the most recent time by which any local-realist influences could have exploited the "freedom-of-choice" loophole to engineer the observed Bell violation, excluding any such mechanism from 96% of the space-time volume of the past light cone of our experiment, extending from the big bang to today.

Satellite-Relayed Intercontinental Quantum Network.

We perform decoy-state quantum key distribution between a low-Earth-orbit satellite and multiple ground stations located in Xinglong, Nanshan, and Graz, which establish satellite-to-ground secure keys with ∼kHz rate per passage of the satellite Micius over a ground station. The satellite thus establishes a secure key between itself and, say, Xinglong, and another key between itself and, say, Graz. Then, upon request from the ground command, Micius acts as a trusted relay. It performs bitwise exclusive or operations between the two keys and relays the result to one of the ground stations. That way, a secret key is created between China and Europe at locations separated by 7600 km on Earth. These keys are then used for intercontinental quantum-secured communication. This was, on the one hand, the transmission of images in a one-time pad configuration from China to Austria as well as from Austria to China. Also, a video conference was performed between the Austrian Academy of Sciences and the Chinese Academy of Sciences, which also included a 280 km optical ground connection between Xinglong and Beijing. Our work clearly confirms the Micius satellite as a robust platform for quantum key distribution with different ground stations on Earth, and points towards an efficient solution for an ultralong-distance global quantum network.

Quantum teleportation over 143 kilometres using active feed-forward.

The quantum internet is predicted to be the next-generation information processing platform, promising secure communication and an exponential speed-up in distributed computation. The distribution of single qubits over large distances via quantum teleportation is a key ingredient for realizing such a global platform. By using quantum teleportation, unknown quantum states can be transferred over arbitrary distances to a party whose location is unknown. Since the first experimental demonstrations of quantum teleportation of independent external qubits, an internal qubit and squeezed states, researchers have progressively extended the communication distance. Usually this occurs without active feed-forward of the classical Bell-state measurement result, which is an essential ingredient in future applications such as communication between quantum computers. The benchmark for a global quantum internet is quantum teleportation of independent qubits over a free-space link whose attenuation corresponds to the path between a satellite and a ground station. Here we report such an experiment, using active feed-forward in real time. The experiment uses two free-space optical links, quantum and classical, over 143 kilometres between the two Canary Islands of La Palma and Tenerife. To achieve this, we combine advanced techniques involving a frequency-uncorrelated polarization-entangled photon pair source, ultra-low-noise single-photon detectors and entanglement-assisted clock synchronization. The average teleported state fidelity is well beyond the classical limit of two-thirds. Furthermore, we confirm the quality of the quantum teleportation procedure without feed-forward by complete quantum process tomography. Our experiment verifies the maturity and applicability of such technologies in real-world scenarios, in particular for future satellite-based quantum teleportation.

Twisted photon entanglement through turbulent air across Vienna.

Photons with a twisted phase front can carry a discrete, in principle, unbounded amount of orbital angular momentum (OAM). The large state space allows for complex types of entanglement, interesting both for quantum communication and for fundamental tests of quantum theory. However, the distribution of such entangled states over large distances was thought to be infeasible due to influence of atmospheric turbulence, indicating a serious limitation on their usefulness. Here we show that it is possible to distribute quantum entanglement encoded in OAM over a turbulent intracity link of 3 km. We confirm quantum entanglement of the first two higher-order levels (with OAM=± 1h and ± 2h). They correspond to four additional quantum channels orthogonal to all that have been used in long-distance quantum experiments so far. Therefore, a promising application would be quantum communication with a large alphabet. We also demonstrate that our link allows access to up to 11 quantum channels of OAM. The restrictive factors toward higher numbers are technical limitations that can be circumvented with readily available technologies.

Teleportation of entanglement over 143 km.

As a direct consequence of the no-cloning theorem, the deterministic amplification as in classical communication is impossible for unknown quantum states. This calls for more advanced techniques in a future global quantum network, e.g., for cloud quantum computing. A unique solution is the teleportation of an entangled state, i.e., entanglement swapping, representing the central resource to relay entanglement between distant nodes. Together with entanglement purification and a quantum memory it constitutes a so-called quantum repeater. Since the aforementioned building blocks have been individually demonstrated in laboratory setups only, the applicability of the required technology in real-world scenarios remained to be proven. Here we present a free-space entanglement-swapping experiment between the Canary Islands of La Palma and Tenerife, verifying the presence of quantum entanglement between two previously independent photons separated by 143 km. We obtained an expectation value for the entanglement-witness operator, more than 6 SDs beyond the classical limit. By consecutive generation of the two required photon pairs and space-like separation of the relevant measurement events, we also showed the feasibility of the swapping protocol in a long-distance scenario, where the independence of the nodes is highly demanded. Because our results already allow for efficient implementation of entanglement purification, we anticipate our research to lay the ground for a fully fledged quantum repeater over a realistic high-loss and even turbulent quantum channel.