Single photons with helical phase structures may carry a quantized amount of orbital angular momentum (OAM), and their entanglement is important for quantum information science and fundamental tests of quantum theory. Because there is no theoretical upper limit on how many quanta of OAM a single photon can carry, it is possible to create entanglement between two particles with an arbitrarily high difference in quantum number. By transferring polarization entanglement to OAM with an interferometric scheme, we generate and verify entanglement between two photons differing by 600 in quantum number. The only restrictive factors toward higher numbers are current technical limitations. We also experimentally demonstrate that the entanglement of very high OAM can improve the sensitivity of angular resolution in remote sensing.

SUMMARYIndistinguishable quantum states interfere, but the mere possibility of obtaining information that could distinguish between overlapping states inhibits quantum interference. Quantum interference imaging can outperform classical imaging or even have entirely new features.Here, we introduce and experimentally demonstrate a quantum imaging concept that relies on the indistinguishability of the possible sources of a photon that remains undetected. Our experiment uses pair creation in two separate down-conversion crystals. While the photons passing through the object are never detected, we obtain images exclusively with the sister photons that do not interact with the object. Therefore the object to be imaged can be either opaque or invisible to the detected photons. Moreover, our technique allows the probe wavelength to be chosen in a range for which suitable sources and/or detectors are unavailable. Our experiment is a prototype in quantum information where knowledge can be extracted by and about a photon that is never detected.2

In contrast to classical physics, quantum theory demands that not all properties can be simultaneously well defined; the Heisenberg uncertainty principle is a manifestation of this fact. Alternatives have been explored--notably theories relying on joint probability distributions or non-contextual hidden-variable models, in which the properties of a system are defined independently of their own measurement and any other measurements that are made. Various deep theoretical results imply that such theories are in conflict with quantum mechanics. Simpler cases demonstrating this conflict have been found and tested experimentally with pairs of quantum bits (qubits). Recently, an inequality satisfied by non-contextual hidden-variable models and violated by quantum mechanics for all states of two qubits was introduced and tested experimentally. A single three-state system (a qutrit) is the simplest system in which such a contradiction is possible; moreover, the contradiction cannot result from entanglement between subsystems, because such a three-state system is indivisible. Here we report an experiment with single photonic qutrits which provides evidence that no joint probability distribution describing the outcomes of all possible measurements--and, therefore, no non-contextual theory--can exist. Specifically, we observe a violation of the Bell-type inequality found by Klyachko, Can, Binicioğlu and Shumovsky. Our results illustrate a deep incompatibility between quantum mechanics and classical physics that cannot in any way result from entanglement.

Entangled quantum systems have properties that have fundamentally overthrown the classical worldview. Increasing the complexity of entangled states by expanding their dimensionality allows the implementation of novel fundamental tests of nature, and moreover also enables genuinely new protocols for quantum information processing. Here we present the creation of a (100 × 100)-dimensional entangled quantum system, using spatial modes of photons. For its verification we develop a novel nonlinear criterion which infers entanglement dimensionality of a global state by using only information about its subspace correlations. This allows very practical experimental implementation as well as highly efficient extraction of entanglement dimensionality information. Applications in quantum cryptography and other protocols are very promising.photonic spatial modes | quantum optics | Schmidt rank | entanglement witness Q uantum entanglement of distant particles leads to correlations that cannot be explained in a local realistic way (1-3). To obtain a deeper understanding of entanglement itself, as well as its application in various quantum information tasks, increasing the complexity of entangled systems is important. Essentially, this can be done in two ways. The first method is to increase the number of particles involved in the entanglement (4). The alternative method is to increase the entanglement dimensionality of a system.Here we focus on the latter one, namely on the dimension of the entanglement. The text is structured as follows. After a short review of properties and previous experiments, we present a unique method to verify high-dimensional entanglement. Then we show how we experimentally create our high-dimensional two-photon entangled state. We analyze this state with our method and verify a 100 × 100-dimensional entangled quantum system. We conclude with a short outlook to potential future investigations.High-dimensional entanglement provides a higher information density than conventional two-dimensional (qubit) entangled states, which has important advantages in quantum communication. First, it can be used to increase the channel capacity via superdense coding (5). Second, high-dimensional entanglement enables the implementation of quantum communication tasks in regimes where mere qubit entanglement does not suffice. This involves situations with a high level of noise from the environment (6, 7), or quantum cryptographic systems where an eavesdropper has manipulated the random number generator involved (8). Moreover, the entangled dimensions of the whole Hilbert space also play a very interesting role in quantum computation: high-dimensional systems can be used to simplify the implementation of quantum logic (9). Furthermore, it has been found recently (10) that any continuous measure of entanglement (such as concurrence, entanglement of formation, or negativity) can be very small, while the quantum system still permits an exponential computation speedup over classical machines. This is not the case for the dim...

Quantum mechanics predicts a number of, at first sight, counterintuitive phenomena. It therefore remains a question whether our intuition is the best way to find new experiments. Here, we report the development of the computer algorithm Melvin which is able to find new experimental implementations for the creation and manipulation of complex quantum states. Indeed, the discovered experiments extensively use unfamiliar and asymmetric techniques which are challenging to understand intuitively. The results range from the first implementation of a high-dimensional Greenberger-Horne-Zeilinger state, to a vast variety of experiments for asymmetrically entangled quantum states-a feature that can only exist when both the number of involved parties and dimensions is larger than 2. Additionally, new types of high-dimensional transformations are found that perform cyclic operations. Melvin autonomously learns from solutions for simpler systems, which significantly speeds up the discovery rate of more complex experiments. The ability to automate the design of a quantum experiment can be applied to many quantum systems and allows the physical realization of quantum states previously thought of only on paper.

The principles of quantum optics have yielded a plethora of ideas to surpass the classical limitations of sensitivity and resolution in optical microscopy. While some ideas have been applied in proof-of-principle experiments, imaging a biological sample has remained challenging mainly due to the inherently weak signal measured and the fragility of quantum states of light. In principle, however, these quantum protocols can add new information without sacrificing the classical information and can therefore enhance the capabilities of existing super-resolution techniques. Image scanning microscopy (ISM), a recent addition to the family of super-resolution methods, generates a robust resolution enhancement without sacrificing the signal level. Here we introduce quantum image scanning microscopy (Q-ISM): combining ISM with the measurement of quantum photon correlation allows increasing the resolution of ISM up to two-fold, four times beyond the diffraction limit. We introduce the Q-ISM principle and obtain super-resolved optical images of a biological sample stained with fluorescent quantum dots using photon antibunching, a quantum effect, as a resolution enhancing contrast mechanism. Main TextThe diffraction limit, as formulated by Abbe, sets the attainable resolution in far-field optical microscopy to about half of the visible wavelength 1 , hindering its applicability in life science studies at very small scales. Over the past two decades, several super-resolution methods have successfully overcome the diffraction limit, including emission depletion microscopy, localization microscopy and structured illumination microscopy 2-6 . The continuous and rapid improvement in detector technology has enabled two more recent developments in the field of super-resolution microscopy, which are the center of this work: quantum super-resolution microscopy and image scanning microscopy (ISM). As for the first, a surge of interest in super-resolution imaging based on quantum optics concepts 7-13 , inspired and facilitated by the progress in high temporal resolution imagers, resulted in a few successful proof-of-principle demonstrations 7,8,14 . The second, ISM, relies on a small array of fast detector and offers a two-fold enhancement of resolution 15,16 . Since ISM is compatible with a standard confocal microscope architecture it has already been integrated into commercial products.While all super-resolution modalities violate at least one of the basic assumptions of the Abbe theory, many rely on breaking more than one. For instance, stimulated emission depletion (STED) and saturated structured illumination microscopy (SSIM) breach both the assumption of a linear response of a fluorophore to the excitation light and that of a uniform illumination field 17,18 . In contrast, the few demonstrations of quantum super-resolution microscopy 7,8,14 relied solely on violating the implicit assumption, underlying Abbe's derivation, that light behaves as waves rather than particles. ISM, as well, depends on violating a single assumption, a u...

Quantum Entanglement is widely regarded as one of the most prominent features of quantum mechanics and quantum information science. Although, photonic entanglement is routinely studied in many experiments nowadays, its signature has been out of the grasp for real-time imaging. Here we show that modern technology, namely triggered intensified charge coupled device (ICCD) cameras are fast and sensitive enough to image in real-time the effect of the measurement of one photon on its entangled partner. To quantitatively verify the non-classicality of the measurements we determine the detected photon number and error margin from the registered intensity image within a certain region. Additionally, the use of the ICCD camera allows us to demonstrate the high flexibility of the setup in creating any desired spatial-mode entanglement, which suggests as well that visual imaging in quantum optics not only provides a better intuitive understanding of entanglement but will improve applications of quantum science.

Photonics has become a mature field of quantum information science, where integrated optical circuits offer a way to scale the complexity of the set-up as well as the dimensionality of the quantum state. On photonic chips, paths are the natural way to encode information. To distribute those high-dimensional quantum states over large distances, transverse spatial modes, like orbital angular momentum possessing Laguerre Gauss modes, are favourable as flying information carriers. Here we demonstrate a quantum interface between these two vibrant photonic fields. We create three-dimensional path entanglement between two photons in a nonlinear crystal and use a mode sorter as the quantum interface to transfer the entanglement to the orbital angular momentum degree of freedom. Thus our results show a flexible way to create high-dimensional spatial mode entanglement. Moreover, they pave the way to implement broad complex quantum networks where high-dimensionally entangled states could be distributed over distant photonic chips.