Generation and confirmation of a (100 x 100)-dimensional entangled quantum system

Experimental realization of a three-photon asymmetric maximally entangled state and its application to quantum state transfer

Quantum entanglement is crucial for quantum information processing, prominently used in quantum communication, computation, and metrology. Recent studies have shifted toward high-dimensional entangled states, offering greater information capacity and enabling more complex applications. Here, we experimentally prepared a three-photon asymmetric maximally entangled state, comprising two two-dimensional photons and one four-dimensional photon. Using this state, we conducted a proof-of-principle experiment, successfully transferring a four-dimensional quantum state from two photons to another photon with fidelities ranging from 0.78 to 0.86. These results exceed theoretical limits, demonstrating genuine four-dimensional quantum state transfer. The asymmetric entangled state demonstrated here holds promise for future quantum networks as a quantum interface facilitating information transfer across quantum systems with different dimensions.

All-fiber function devices for twisted lights

Lights carrying orbital angular momentum (OAM), also called twisted lights, have been applied in fields of optical manipulation, imaging, quantum communication, and mode-division-multiplexing (MDM) optical communication systems. Traditional approaches for manipulating twisted lights carrying OAM in free space paths such as Q-plates, spiral phase plates (SPPs), and spatial light modulators (SLMs) that are usually affected by diffraction effect and imperfect alignment between different optical components, limiting the practical applications of twisted lights. Here we design, fabricated, and package all-fiber function devices for twisted light carrying OAM such as all-fiber broadband OAM generator, all-fiber OAM (de)multiplexer, all-fiber OAM & WDM coupler, and all-fiber OAM 1 × 2 coupler. Base on coupled mode theory and phase-matching condition, twisted light can be generated and detected by pre-tapered single mode fiber (SMF) fusing with multi-mode fiber (MMF). The results show that the proposed all-fiber function devices for twist light have large working broadband (at least C band), high purity (above 95%), and low insert loss (less than 3 dB). The proposed devices will open a reliable way for twisted light applied in optical fiber communications and optical interconnections.

Highly Efficient Storage of 25-Dimensional Photonic Qudit in a Cold-Atom-Based Quantum Memory

Building an efficient quantum memory in high-dimensional Hilbert spaces is one of the fundamental requirements for establishing high-dimensional quantum repeaters, where it offers many advantages over two-dimensional quantum systems, such as a larger information capacity and enhanced noise resilience. To date, it remains a challenge to develop an efficient high-dimensional quantum memory. Here, we experimentally realize a quantum memory that is operational in Hilbert spaces of up to 25 dimensions with a storage efficiency of close to 60% and a fidelity of 84.2±0.6%. The proposed approach exploits the spatial-mode-independent interaction between atoms and photons which are encoded in transverse-size-invariant vortex modes. In particular, our memory features uniform storage efficiency and low crosstalk disturbance for 25 individual spatial modes of photons, thus allowing the storing of qudit states programmed from 25 eigenstates within the high-dimensional Hilbert spaces. These results have great prospects for the implementation of long-distance high-dimensional quantum networks and quantum information processing.

Resource-Efficient High-Dimensional Entanglement Detection via Symmetric Projections

We introduce two families of criteria for detecting and quantifying the entanglement of a bipartite quantum state of arbitrary local dimension. The first is based on measurements in mutually unbiased bases and the second is based on equiangular measurements. Both criteria give a qualitative result in terms of the state's entanglement dimension and a quantitative result in terms of its fidelity with the maximally entangled state. The criteria are universally applicable since no assumptions on the state are required. Moreover, the experimenter can control the trade-off between resource-efficiency and noise-tolerance by selecting the number of measurements performed. For paradigmatic noise models, we show that only a small number of measurements are necessary to achieve nearly-optimal detection in any dimension. The number of global product projections scales only linearly in the local dimension, thus paving the way for detection and quantification of very high-dimensional entanglement.

Radial-mode sensitive probe beam in the rotational Doppler effect

The rotational Doppler effect (RDE) attracts much attention in various research areas, from acoustics to optics. The observation of RDE mostly depends on the orbital angular momentum of the probe beam, while the impression of radial mode is ambiguous. To clarify the role of radial modes in RDE detection, we reveal the mechanism of interaction between probe beams and rotating objects based on complete Laguerre-Gaussian (LG) modes. It is theoretically and experimentally proved that radial LG modes play a crucial role in RDE observation because of topological spectroscopic orthogonality between probe beams and objects. We enhance the probe beam by employing multiple radial LG modes, which makes the RDE detection sensitive to objects containing complicated radial structures. In addition, a specific method to estimate the efficiency of various probe beams is proposed. This work has the potential to modify RDE detection method and take the related applications to a new platform.

Two-Measurement Tomography of High-Dimensional Orbital Angular Momentum Entanglement

High-dimensional (HD) entanglement enables an encoding of more bits than in the two-dimensional case and promises to increase communication capacity over quantum channels and to improve robustness to noise. In practice, however, one of the central challenges is to devise efficient methods to quantify the HD entanglement explicitly. Full quantum state tomography is a standard technology to obtain all the information about the quantum state, but it becomes impractical because the required measurements increase exponentially with the dimension in HD systems. Hence, it is highly anticipated that a new method will be found for characterizing the HD entanglement with as few measurements as possible and without introducing unwarranted assumptions. Here, we present and demonstrate a scan-free tomography method independent of dimension, which only requires two measurements for the characterization of two-photon HD orbital angular momentum (OAM) entanglement. Taking Laguerre-Gaussian modes of photons as an example, the density matrices of OAM entangled states are experimentally reconstructed with very high fidelity. Our method is also generalized to the mixed HD OAM entanglement. Our results provide realistic approaches for quantifying more complex OAM entanglement in many scientific and engineering fields such as multiphoton HD quantum systems and quantum process tomography.

Experimental Realization of Two Qutrits Gate with Tunable Coupling in Superconducting Circuits

Gate-based quantum computation has been extensively investigated using quantum circuits based on qubits. In many cases, such qubits are actually made out of multilevel systems but with only two states being used for computational purpose. While such a strategy has the advantage of being in line with the common binary logic, it in some sense wastes the ready-for-use resources in the large Hilbert space of these intrinsic multidimensional systems. Quantum computation beyond qubits (e.g., using qutrits or qudits) has thus been discussed and argued to be more efficient than its qubit counterpart in certain scenarios. However, one of the essential elements for qutrit-based quantum computation, two-qutrit quantum gate, remains a major challenge. In this Letter, we propose and demonstrate a highly efficient and scalable two-qutrit quantum gate in superconducting quantum circuits. Using a tunable coupler to control the cross-Kerr coupling between two qutrits, our scheme realizes a two-qutrit conditional phase gate with fidelity 89.3% by combining simple pulses applied to the coupler with single-qutrit operations. We further use such a two-qutrit gate to prepare an EPR state of two qutrits with a fidelity of 95.5%. Our scheme takes advantage of a tunable qutrit-qutrit coupling with a large on:off ratio. It therefore offers both high efficiency and low crosstalk between qutrits, thus being friendly for scaling up. Our Letter constitutes an important step toward scalable qutrit-based quantum computation.

Optical mode conversion via spatiotemporally modulated atomic susceptibility

Light is an excellent medium for both classical and quantum information transmission due to its speed, manipulability, and abundant degrees of freedom into which to encode information. Recently, space-division multiplexing has gained attention as a means to substantially increase the rate of information transfer by utilizing sets of infinite-dimensional propagation eigenmodes such as the Laguerre-Gaussian "donut" modes. Encoding in these high-dimensional spaces necessitates devices capable of manipulating photonic degrees of freedom with high efficiency. In this work, we demonstrate controlling the optical susceptibility of an atomic sample can be used as powerful tool for manipulating the degrees of freedom of light that pass through the sample. Utilizing this tool, we demonstrate photonic mode conversion between two Laguerre-Gaussian modes of a twisted optical cavity with high efficiency. We spatiotemporally modulate the optical susceptibility of an atomic sample that sits at the cavity waist using an auxiliary Stark-shifting beam, in effect creating a mode-coupling optic that converts modes of orbital angular momentum l = 3 → l = 0. The internal conversion efficiency saturates near unity as a function of the atom number and modulation beam intensity, finding application in topological few-body state preparation, quantum communication, and potential development as a flexible tabletop device.

Towards higher-dimensional structured light

Structured light refers to the arbitrarily tailoring of optical fields in all their degrees of freedom (DoFs), from spatial to temporal. Although orbital angular momentum (OAM) is perhaps the most topical example, and celebrating 30 years since its connection to the spatial structure of light, control over other DoFs is slowly gaining traction, promising access to higher-dimensional forms of structured light. Nevertheless, harnessing these new DoFs in quantum and classical states remains challenging, with the toolkit still in its infancy. In this perspective, we discuss methods, challenges, and opportunities for the creation, detection, and control of multiple DoFs for higher-dimensional structured light. We present a roadmap for future development trends, from fundamental research to applications, concentrating on the potential for larger-capacity, higher-security information processing and communication, and beyond.

Manipulating the symmetry of transverse momentum entangled biphoton states

Bell states are a fundamental resource in photonic quantum information processing. These states have been generated successfully in many photonic degrees of freedom. Their manipulation, however, in the momentum space remains challenging. Here, we present a scheme for engineering the symmetry of two-photon states entangled in the transverse momentum degree of freedom through the use of a spatially variable phase object. We demonstrate how a Hong-Ou-Mandel interferometer must be constructed to verify the symmetry in momentum entanglement via photon "bunching/anti-bunching" observation. We also show how this approach allows generating states that acquire an arbitrary phase under the exchange operation.

Measuring dimensionality and purity of high-dimensional entangled states

High-dimensional entangled states are promising candidates for increasing the security and encoding capacity of quantum systems. While it is possible to witness and set bounds for the entanglement, precisely quantifying the dimensionality and purity in a fast and accurate manner remains an open challenge. Here, we report an approach that simultaneously returns the dimensionality and purity of high-dimensional entangled states by simple projective measurements. We show that the outcome of a conditional measurement returns a visibility that scales monotonically with state dimensionality and purity, allowing for quantitative measurements for general photonic quantum systems. We illustrate our method using two separate bases, the orbital angular momentum and pixels bases, and quantify the state dimensionality by a variety of definitions over a wide range of noise levels, highlighting its usefulness in practical situations. Importantly, the number of measurements needed in our approach scale linearly with dimensions, reducing data acquisition time significantly. Our technique provides a simple, fast and direct measurement approach.

Full-mode characterization of correlated photon pairs generated in spontaneous downconversion

Spontaneous parametric downconversion is the primary source to generate entangled photon pairs in quantum photonics laboratories. Depending on the experimental design, the generated photon pairs can be correlated in the frequency spectrum, polarization, position-momentum, and spatial modes. Exploring the spatial modes' correlation has hitherto been limited to the polar coordinates' azimuthal angle, and a few attempts to study Walsh mode's radial states. Here, we study the full-mode correlation, on a Laguerre-Gauss basis, between photon pairs generated in a type-I crystal. Furthermore, we explore the effect of a structured pump beam possessing different spatial modes onto bi-photon spatial correlation. Finally, we use the capability to project over arbitrary spatial mode superpositions to perform the bi-photon state's full quantum tomography in a 16-dimensional subspace.

Initializing 214 Pure 14-Qubit Entangled Nuclear Spin States in a Hyperpolarized Molecular Solid

Quantum entanglement has been realized on a variety of physical platforms such as quantum dots, trapped atomic ions, and superconductors. Here we introduce specific molecular solids as promising alternative platforms. Our model system is triplet pentacene in a host single crystal at level anticrossing (LAC) conditions. First, a laser pulse generates the triplet state and initiates entanglement between an electron spin and 14 hyperfine coupled proton spins (quantum bits or qubits). This gives rise to large nuclear spin polarization. Subsequently, a resonant high-power microwave (mw) pulse disentangles the electron spin from the nuclear spins. Simultaneously, high-dimensional multiqubit entanglement is formed among the proton spins. We verified the initialization of 2¹⁴ pure 14-qubit entangled nuclear spin states with an average degree of entanglement of E_av = 0.77 ± 0.03. These results pave the way for large-scale quantum information processing with more than 10 000 multiqubit entangled states corresponding to computational (Hilbert) space dimensions of dim >10⁵³.

Entanglement protection of Ince-Gauss modes in atmospheric turbulence using adaptive optics

In this paper, we describe the study of the faithful propagation of entangled orbital angular momentum states of light under atmospheric turbulence. The spatial mode is encoded in the Ince-Gauss modes that constitute a complete family of exact and orthogonal solutions of the paraxial wave equation in an elliptic coordinate system. Adaptive optics is employed to protect the entanglement from degradation, in which the threshold of turbulence strength could be enhanced for a reliable entanglement distribution. We find that the evolution of entanglements relies on ellipticity and shows the opposite trend when adopting adaptive optics. The turbulence strengths, at which the concurrences of various entangled states become zero, are different without adaptive optics but almost the same with adaptive optics. The trace of the density matrix is independent of the different ellipticity with or without adaptive optics. We believe that this investigation is useful for long-distance quantum communications and quantum networks using orbital angular momentum as information carriers.

Experimental High-Dimensional Quantum Teleportation

Quantum teleportation provides a way to transmit unknown quantum states from one location to another. In the quantum world, multilevel systems which enable high-dimensional systems are more prevalent. Therefore, to completely rebuild the quantum states of a single particle remotely, one needs to teleport multilevel (high-dimensional) states. Here, we demonstrate the teleportation of high-dimensional states in a three-dimensional six-photon system. We exploit the spatial mode of a single photon as the high-dimensional system, use two auxiliary entangled photons to realize a deterministic three-dimensional Bell state measurement. The fidelity of teleportation process matrix is F=0.596±0.037. Through this process matrix, we can prove that our teleportation is both nonclassical and genuine three dimensional. Our work paves the way to rebuild complex quantum systems remotely and to construct complex quantum networks.

Boosting Entanglement Generation in Down-Conversion with Incoherent Illumination

Entangled photons produced by spontaneous parametric down-conversion have been of paramount importance for our current understanding of quantum mechanics and advances in quantum information. In this process, the quantum correlations of the down-converted photons are governed by the optical properties of the pump beam illuminating the nonlinear crystal. Extensively, the pump beam has been modeled by either coherent beams or by the well-known Gaussian-Schell model, which leads to the natural conclusion that a high degree of optical coherence is required for the generation of highly entangled states. Here, we show that when a novel class of partially coherent Gaussian pump beams is considered, a distinct type of quantum state can be generated for which the amount of entanglement increases inversely with the degree of coherence of the pump beam. This leads to highly incoherent yet highly entangled multiphoton states, which should have interesting consequences for photonic quantum information science.

Path identity as a source of high-dimensional entanglement

Quantum entanglement amounts to an extremely strong link between two distant particles, a link so strong that it eludes any classical description and so unsettling that Albert Einstein described it as “spooky action at a distance.” Today, entanglement is not only a subject of fundamental research, but also a workhorse of emerging quantum technologies. In our current work we experimentally demonstrate a completely different method of entanglement generation. Unlike many traditional methods, where entanglement arises due to conservation of a physical quantity, such as momentum, in our method it is rather a consequence of indistinguishability of several particle-generating processes. This approach, where each process effectively adds one dimension to the entangled state, allows for a high degree of customizability.

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.

An inherently infinite-dimensional quantum correlation

Bell's theorem, a landmark result in the foundations of physics, establishes that quantum mechanics is a non-local theory. It asserts, in particular, that two spatially separated, but entangled, quantum systems can be correlated in a way that cannot be mimicked by classical systems. A direct operational consequence of Bell's theorem is the existence of statistical tests which can detect the presence of entanglement. Remarkably, certain correlations not only witness entanglement, but they give quantitative bounds on the minimum dimension of quantum systems attaining them. In this work, we show that there exists a correlation which is not attainable by quantum systems of any arbitrary finite dimension, but is attained exclusively by infinite-dimensional quantum systems (such as infinite-level systems arising from quantum harmonic oscillators). This answers the long-standing open question about the existence of a finite correlation witnessing infinite entanglement.

Vector Vortex Beam Emitter Embedded in a Photonic Chip

Vector vortex beams simultaneously carrying spin and orbital angular momentum of light promise additional degrees of freedom for modern optics and emerging resources for both classical and quantum information technologies. The inherently infinite dimensions can be exploited to enhance data capacity for sustaining the unprecedented growth in big data and internet traffic and can be encoded to build quantum computing machines in high-dimensional Hilbert space. So far, much progress has been made in the emission of vector vortex beams from a chip surface into free space; however, the generation of vector vortex beams inside a photonic chip has not been realized yet. Here, we demonstrate the first vector vortex beam emitter embedded in a photonic chip by using femtosecond laser direct writing. We achieve a conversion of vector vortex beams with an efficiency up to 30% and scalar vortex beams with an efficiency up to 74% from Gaussian beams. We also present an expanded coupled-mode model for understanding the mode conversion and the influence of the imperfection in fabrication. The fashion of embedded generation makes vector vortex beams directly ready for further transmission, manipulation, and emission without any additional interconnection. Together with the ability to be integrated as an array, our results may enable vector vortex beams to become accessible inside a photonic chip for high-capacity communication and high-dimensional quantum information processing.

Boson Sampling with 20 Input Photons and a 60-Mode Interferometer in a 10^{14}-Dimensional Hilbert Space

Quantum computing experiments are moving into a new realm of increasing size and complexity, with the short-term goal of demonstrating an advantage over classical computers. Boson sampling is a promising platform for such a goal; however, the number of detected single photons is up to five so far, limiting these small-scale implementations to a proof-of-principle stage. Here, we develop solid-state sources of highly efficient, pure, and indistinguishable single photons and 3D integration of ultralow-loss optical circuits. We perform experiments with 20 pure single photons fed into a 60-mode interferometer. In the output, we detect up to 14 photons and sample over Hilbert spaces with a size up to 3.7×10^{14}, over 10 orders of magnitude larger than all previous experiments, which for the first time enters into a genuine sampling regime where it becomes impossible to exhaust all possible output combinations. The results are validated against distinguishable samplers and uniform samplers with a confidence level of 99.9%.

Quantum image distillation

Imaging with quantum states of light promises advantages over classical approaches in terms of resolution, signal-to-noise ratio, and sensitivity. However, quantum detectors are particularly sensitive sources of classical noise that can reduce or cancel any quantum advantage in the final result. Without operating in the single-photon counting regime, we experimentally demonstrate distillation of a quantum image from measured data composed of a superposition of both quantum and classical light. We measure the image of an object formed under quantum illumination (correlated photons) that is mixed with another image produced by classical light (uncorrelated photons) with the same spectrum and polarization, and we demonstrate near-perfect separation of the two superimposed images by intensity correlation measurements. This work provides a method to mix and distinguish information carried by quantum and classical light, which may be useful for quantum imaging, communications, and security.

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.

Orbital-Angular-Momentum Multiplexed Continuous-Variable Entanglement from Four-Wave Mixing in Hot Atomic Vapor

Multiplexing is crucial for the data-carrying capacity of information communication systems. Orbital angular momentum (OAM) with a topological charge ℓ (ℓ integer) provides a degree of freedom to realize multiplexing. In this Letter, we report an experimental implementation of OAM multiplexed continuous variables (CV) entanglement based on a four-wave mixing (FWM) process, in which 13 pairs of entangled Laguerre-Gauss (LG) modes, LG_{ℓ,pr} and LG_{-ℓ,conj}, are simultaneously and deterministically generated, where ℓ (ℓ integer) is the topological charge corresponding to the OAM mode and pr (conj) indicates a probe (conjugate) beam. In the meanwhile, we experimentally show that there is no entanglement between the modes of LG_{ℓ,pr} and LG_{ℓ,conj} (ℓ≠0). These results clearly confirm the conservation of OAM in the FWM process from the viewpoint of a CV system. In addition, we investigate the entanglement properties of three types of coherent superposition of OAM modes. In the end, we also study the effect of the pump beam radius on the number of OAM multiplexing. Such OAM multiplexed CV entanglement provides a new perspective and platform to study CV quantum information protocols.

Beam profiler network (BPNet): a deep learning approach to mode demultiplexing of Laguerre-Gaussian optical beams

The transverse field profile of light has been recognized as a resource for classical and quantum communications for which reliable methods of sorting or demultiplexing spatial optical modes are required. Here we experimentally demonstrate state-of-the-art mode demultiplexing of Laguerre-Gaussian beams according to both their orbital angular momentum and radial topological numbers using a flow of two concatenated deep neural networks. The first network serves as a transfer function from experimentally generated to ideal numerically generated data, while using a unique "histogram weighted loss" function that solves the problem of images with limited significant information. The second network acts as a spatial-modes classifier. Our method uses only the intensity profile of modes or their superposition, making the phase information redundant.

Influence of pump coherence on the generation of position-momentum entanglement in optical parametric down-conversion

We examine experimentally how the degree of position-momentum entanglement of photon pairs depends on the transverse coherence of the pump beam that excites them in a process of spontaneous parametric down-conversion. Using spatially incoherent light from a light-emitting diode, we obtain strong position correlation of the photons, but we find that transverse momentum correlation, and thus entanglement, is entirely absent. When we continuously vary the degree of spatial coherence on the pump beam, we observe the emergence of stronger momentum correlations and entanglement. We present theoretical arguments that explain our experimental results. Our results shed light on entanglement generation and can be applied to control entanglement for quantum information applications.

Quantifying entanglement in a 68-billion-dimensional quantum state space

Entanglement is the powerful and enigmatic resource central to quantum information processing, which promises capabilities in computing, simulation, secure communication, and metrology beyond what is possible for classical devices. Exactly quantifying the entanglement of an unknown system requires completely determining its quantum state, a task which demands an intractable number of measurements even for modestly-sized systems. Here we demonstrate a method for rigorously quantifying high-dimensional entanglement from extremely limited data. We improve an entropic, quantitative entanglement witness to operate directly on compressed experimental data acquired via an adaptive, multilevel sampling procedure. Only 6,456 measurements are needed to certify an entanglement-of-formation of 7.11 ± .04 ebits shared by two spatially-entangled photons. With a Hilbert space exceeding 68 billion dimensions, we need 20-million-times fewer measurements than the uncompressed approach and 10¹⁸-times fewer measurements than tomography. Our technique offers a universal method for quantifying entanglement in any large quantum system shared by two parties.

Classical simulation of high-dimensional entanglement by non-separable angular-radial modes

An analogous model system for high-dimensional quantum entanglement is proposed, based on the angular and radial degrees of freedom of the improved Laguerre Gaussian mode. Experimentally, we observed strong violations of the Bell-CGLMP inequality for maximally non-separable states of dimension 2 through 10. The results for violations in classical non-separable state are in very good agreement with quantum instance, which illustrates that our scheme can be a useful platform to simulate high-dimensional non-local entanglement. Additionally, we found that the Bell measurements provide sufficient criteria for identifying mode separability in a high-dimensional space. Similar to the two-dimensional spin-orbit non-separable state, the proposed high-dimensional angular-radial non-separable state may provide promising applications for classical and quantum information processing.

Cyclic permutations for qudits in d dimensions

One of the main challenges in quantum technologies is the ability to control individual quantum systems. This task becomes increasingly difficult as the dimension of the system grows. Here we propose a general setup for cyclic permutations Xd in d dimensions, a major primitive for constructing arbitrary qudit gates. Using orbital angular momentum states as a qudit, the simplest implementation of the Xd gate in d dimensions requires a single quantum sorter Sd and two spiral phase plates. We then extend this construction to a generalised Xd(p) gate to perform a cyclic permutation of a set of d, equally spaced values {|[Formula: see text]〉, |[Formula: see text] + p〉, …, |[Formula: see text] + (d - 1)p〉} [Formula: see text] {|[Formula: see text] + p〉, |[Formula: see text] + 2p〉, …, |[Formula: see text]〉}. We find compact implementations for the generalised Xd(p) gate in both Michelson (one sorter Sd, two spiral phase plates) and Mach-Zehnder configurations (two sorters Sd, two spiral phase plates). Remarkably, the number of spiral phase plates is independent of the qudit dimension d. Our architecture for Xd and generalised Xd(p) gate will enable complex quantum algorithms for qudits, for example quantum protocols using photonic OAM states.

Active engineering of four-wave mixing spectral correlations in multiband hollow-core fibers

We demonstrate theoretically and experimentally a high level of control of the four-wave mixing process in an inert gas-filled inhibited-coupling guiding hollow-core photonic crystal fiber. The specific multiple-branch dispersion profile in such fibers allows both correlated and separable bi-photon states to be produced. By controlling the choice of gas and its pressure and the fiber length, we experimentally generate various joint spectral intensity profiles in a stimulated regime that is transferable to the spontaneous regime. The generated profiles may cover both spectrally separable and correlated bi-photon states and feature frequency tuning over tens of THz, demonstrating a large dynamic control that will be very useful when implemented in the spontaneous regime as a photon pair source.

Universal N-Partite d-Level Pure-State Entanglement Witness Based on Realistic Measurement Settings

Entanglement witnesses are operators that are crucial for confirming the generation of specific quantum systems, such as multipartite and high-dimensional states. For this reason, many witnesses have been theoretically derived which commonly focus on establishing tight bounds and exhibit mathematical compactness as well as symmetry properties similar to that of the quantum state. However, for increasingly complex quantum systems, established witnesses have lacked experimental achievability, as it has become progressively more challenging to design the corresponding experiments. Here, we present a universal approach to derive entanglement witnesses that are capable of detecting the presence of any targeted complex pure quantum system and that can be customized towards experimental restrictions or accessible measurement settings. Using this technique, we derive experimentally optimized witnesses that are able to detect multipartite d-level cluster states, and that require only two measurement settings. We present explicit examples for customizing the witness operators given different realistic experimental restrictions, including witnesses for high-dimensional entanglement that use only two-dimensional projection measurements. Our work enables us to confirm the presence of probed quantum states using methods that are compatible with practical experimental realizations in different quantum platforms.

Photonic Gauge Potential in One Cavity with Synthetic Frequency and Orbital Angular Momentum Dimensions

We explore a single degenerate optical cavity supporting a synthetic two-dimensional space, which includes the frequency and the orbital angular momentum (OAM) axes of light. We create the effective gauge potential inside this synthetic space and show that the system exhibits topologically protected one-way edge states along the OAM axis at the boundaries of the frequency dimension. In this synthetic space, we present a robust generation and manipulation of entanglement between the frequency and OAM of photons. Our Letter shows that a higher-dimensional synthetic space involving multiple degrees of freedom of light can be achieved in a "zero-dimensional" spatial structure, pointing towards a unique platform to explore topological photonics and to realize potential applications in optical communications and quantum information processing.

Measurement of the radial mode spectrum of photons through a phase-retrieval method

We propose and demonstrate a simple and easy-to-implement projective-measurement protocol to determine the radial index p of a Laguerre-Gaussian (LGpl) mode. Our method entails converting any specified high-order LGp0 mode into a near-Gaussian distribution that matches the fundamental mode of a single-mode fiber (SMF) through the use of two phase screens (unitary transforms) obtained by applying a phase-retrieval algorithm. The unitary transforms preserve the orthogonality of modes before the SMF and guarantee that our protocol can, in principle, be free of crosstalk. We measure the coupling efficiency of the transformed radial modes to the SMF for different pairs of phase screens. Because of the universality of phase-retrieval methods, we believe that our protocol provides an efficient way of fully characterizing the radial spatial profile of an optical field.

Realization of a scalable Laguerre-Gaussian mode sorter based on a robust radial mode sorter

The transverse structure of light is recognized as a resource that can be used to encode information onto photons and has been shown to be useful to enhance communication capacity as well as resolve point sources in superresolution imaging. The Laguerre-Gaussian (LG) modes form a complete and orthonormal basis set and are described by a radial index p and an orbital angular momentum (OAM) index ℓ. Earlier works have shown how to build a sorter for the radial index p or/and the OAM index ℓ of LG modes, but a scalable and dedicated LG mode sorter which simultaneous determinate p and ℓ is immature. Here we propose and experimentally demonstrate a scheme to accomplish complete LG mode sorting, which consists of a novel, robust radial mode sorter that can be used to couple radial modes to polarizations, an ℓ-dependent phase shifter and an OAM mode sorter. Our scheme is in principle efficient, scalable, and crosstalk-free, and therefore has potential for applications in optical communications, quantum information technology, superresolution imaging, and fiber optics.

Mapping Twisted Light into and out of a Photonic Chip

Twisted light carrying orbital angular momentum (OAM) provides an additional degree of freedom for modern optics and an emerging resource for both classical and quantum information technologies. Its inherently infinite dimensions can potentially be exploited by using mode multiplexing to enhance data capacity for sustaining the unprecedented growth in big data and internet traffic and can be encoded to build large-scale quantum computing machines in high-dimensional Hilbert space. While the emission of twisted light from the surface of integrated devices to free space has been widely investigated, the transmission and processing inside a photonic chip remain to be addressed. Here, we present the first laser-direct-written waveguide being capable of supporting OAM modes and experimentally demonstrate a faithful mapping of twisted light into and out of a photonic chip. The states OAM_{0}, OAM_{-1}, OAM_{+1}, and their superpositions can transmit through the photonic chip with a total efficiency up to 60% with minimal crosstalk. In addition, we present the transmission of quantum twisted light states of single photons and measure the output states with single-photon imaging. Our results may add OAM as a new degree of freedom to be transmitted and manipulated in a photonic chip for high-capacity communication and high-dimensional quantum information processing.

Classically high-dimensional correlation: simulation of high-dimensional entanglement

Classical correlation, akin to the entanglement of quantum states, has been proven to bear a great promise in classical and quantum systems, such as enhancing measurement precision and characterizing quantum channels. Despite numerous successful applications of such correlation, it is strictly limited to two orthogonal bases and fails to further extend its dimensionality in practice. Here, we report a classically high-dimensional correlation, which is mathematically equivalent to its quantum counterparts and can be used to simulate the violations of the high-dimensional Bell inequalities. Moreover, we also show theoretically that quantum channels with high-dimensional quantum states can be characterized robustly using our scheme when a one-sided channel is perturbed by a turbulent atmosphere. This means that our results not only provide new physical insights into the notion of classical correlation, but also show potential applications in high-dimensional quantum information processing.

Measuring azimuthal and radial modes of photons

With the emergence of the field of quantum communications, the appropriate choice of photonic degrees of freedom used for encoding information is of paramount importance. Highly precise techniques for measuring the polarisation, frequency, and arrival time of a photon have been developed. However, the transverse spatial degree of freedom still lacks a measurement scheme that allows the reconstruction of its full transverse structure with a simple implementation and a high level of accuracy. Here we show a method to measure the azimuthal and radial modes of Laguerre-Gaussian beams with a greater than 99 % accuracy, using a single phase screen. We compare our technique with previous commonly used methods and demonstrate the significant improvements it presents for quantum key distribution and state tomography of high-dimensional quantum states of light. Moreover, our technique can be readily extended to any arbitrary family of spatial modes, such as mutually unbiased bases, Hermite-Gauss, and Ince-Gauss. Our scheme will significantly enhance existing quantum and classical communication protocols that use the spatial structure of light, as well as enable fundamental experiments on spatial-mode entanglement to reach their full potential.

Experimental realization of path-polarization hybrid high-dimensional pure state

High-dimensional entanglement offers promising perspectives in quantum information science. However, how to generate high-quality high-dimensional entanglement and control it efficiently is still a challenge. Here, we experimentally demonstrate a polarization-path hybrid high-dimensional entangled two-photon source with extremely high quality. Based on stable interferometers, we measured fidelities exceeding 0.99 for both three-dimensional and four-dimensional maximal entanglement. The experimental setup can also be used to prepare arbitrary high-dimensional pure state and can be efficiently extended to even higher dimensional systems. Our new source will shed new light on high-dimensional quantum information processes.

Spatially dependent atom-photon entanglement

The atom-photon entanglement using the Laguerre-Gaussian (LG) beams is studied in the closed-loop three-level V-type quantum systems. We consider two schemes with near-degenerate and non-degenerate upper levels: in the first, the effect of the quantum interference due to the spontaneous emission is taken into account and in the second, a microwave plane wave is applied to the upper levels transition. It is shown that the atom-photon entanglement in both schemes depends on the intensity profile as well as the orbital angular momentum (OAM) of the applied fields so that the various spatially dependent entanglement patterns can be generated by Laguerre-Gaussian beams with different OAMs. However, due to the zero intensity,no entanglement appears in the center of the optical vortex beams. As a result, the entanglement between dressed atom and its spontaneous emissions in different points of the atomic vapor cell can be controlled by the OAM of the applied fields. Moreover, our numerical results show that the number of the local maximum degree of entanglement (DEM) peaks depends on the OAM of the applied fields. The degrees of freedom for OAM play a crucial role in spatially dependent atom-photon entanglement in such a way that it may possess broad applications in high-dimensional quantum information processing and data storage.

Manipulating orbital angular momentum entanglement by using the Heisenberg uncertainty principle

Orbital angular momentum entanglement (OAM) is one of the very intriguing topics in quantum physics. In addition to discovering and exploring its underlying mechanics, recent studies have also demonstrated a progress towards expanding degree of its entanglement. In this paper, we explore OAM entanglement by applying the Heisenberg uncertainty principle to the quantum position correlation within the azimuthal region. In particular, we decompose the pump light into a set of pump cone states characterized by their radii. The OAM entanglement can then be manipulated by controlling the radius of the pump cone state, the length of the nonlinear crystal and also the OAM carried by the pump field. That is followed by a detailed discussion and analysis. Such an exploration not only bring us a deeper understanding of OAM entanglement, but also help us to implement the high-dimensional quantum information tasks based on OAM entanglement.

Integrated design of pi/2 converter and its experimental performance

Transverse modes of light have been widely exploited in both classical and quantum optics in recent years. Among the devices to manipulate the transverse modes of light, a π/2 converter is a fundamental and important one that analogs to the quarter-wave plate in the polarization degree of freedom. While a π/2 converter is typically achieved by a pair of well-adjusted cylindrical lenses, it suffers from complexity in its installation and adjustment, which strongly limits its practical applications. In this paper an integrated design of a π/2 converter is reported. We compute the necessary parameters for manufacturing according to refractive theory of a cylindrical surface. Based on the change of refractive indices, we simulate the response of Gouy phase versus wavelengths. We also implement an experiment to verify the conversion between Laguerre-Gaussian modes and Hermite-Gaussian modes by using our compact π/2 converter to confirm its simple adjustment and reliable performance in practice.

Beating the channel capacity limit for superdense coding with entangled ququarts

Quantum superdense coding protocols enhance channel capacity by using shared quantum entanglement between two users. The channel capacity can be as high as 2 when one uses entangled qubits. However, this limit can be surpassed by using high-dimensional entanglement. We report an experiment that exceeds the limit using high-quality entangled ququarts with fidelities up to 0.98, demonstrating a channel capacity of 2.09 ± 0.01. The measured channel capacity is also higher than that obtained when transmitting only one ququart. We use the setup to transmit a five-color image with a fidelity of 0.952. Our experiment shows the great advantage of high-dimensional entanglement and will stimulate research on high-dimensional quantum information processes.

Uncertainty Relations for Coarse-Grained Measurements: An Overview

Uncertainty relations involving incompatible observables are one of the cornerstones of quantum mechanics. Aside from their fundamental significance, they play an important role in practical applications, such as detection of quantum correlations and security requirements in quantum cryptography. In continuous variable systems, the spectra of the relevant observables form a continuum and this necessitates the coarse graining of measurements. However, these coarse-grained observables do not necessarily obey the same uncertainty relations as the original ones, a fact that can lead to false results when considering applications. That is, one cannot naively replace the original observables in the uncertainty relation for the coarse-grained observables and expect consistent results. As such, several uncertainty relations that are specifically designed for coarse-grained observables have been developed. In recognition of the 90th anniversary of the seminal Heisenberg uncertainty relation, celebrated last year, and all the subsequent work since then, here we give a review of the state of the art of coarse-grained uncertainty relations in continuous variable quantum systems, as well as their applications to fundamental quantum physics and quantum information tasks. Our review is meant to be balanced in its content, since both theoretical considerations and experimental perspectives are put on an equal footing.

Certifying an Irreducible 1024-Dimensional Photonic State Using Refined Dimension Witnesses

We report on a new class of dimension witnesses, based on quantum random access codes, which are a function of the recorded statistics and that have different bounds for all possible decompositions of a high-dimensional physical system. Thus, it certifies the dimension of the system and has the new distinct feature of identifying whether the high-dimensional system is decomposable in terms of lower dimensional subsystems. To demonstrate the practicability of this technique, we used it to experimentally certify the generation of an irreducible 1024-dimensional photonic quantum state. Therefore, certifying that the state is not multipartite or encoded using noncoupled different degrees of freedom of a single photon. Our protocol should find applications in a broad class of modern quantum information experiments addressing the generation of high-dimensional quantum systems, where quantum tomography may become intractable.

Massively Parallel Coincidence Counting of High-Dimensional Entangled States

Entangled states of light are essential for quantum technologies and fundamental tests of physics. Current systems rely on entanglement in 2D degrees of freedom, e.g., polarization states. Increasing the dimensionality provides exponential speed-up of quantum computation, enhances the channel capacity and security of quantum communication protocols, and enables quantum imaging; unfortunately, characterizing high-dimensional entanglement of even bipartite quantum states remains prohibitively time-consuming. Here, we develop and experimentally demonstrate a new theory of camera detection that leverages the massive parallelization inherent in an array of pixels. We show that a megapixel array, for example, can measure a joint Hilbert space of 10¹² dimensions, with a speed-up of nearly four orders-of-magnitude over traditional methods. The technique uses standard geometry with existing technology, thus removing barriers of entry to quantum imaging experiments, generalizes readily to arbitrary numbers of entangled photons, and opens previously inaccessible regimes of high-dimensional quantum optics.

General Model of Photon-Pair Detection with an Image Sensor

We develop an analytic model that relates intensity correlation measurements performed by an image sensor to the properties of photon pairs illuminating it. Experiments using an effective single-photon counting camera, a linear electron-multiplying charge-coupled device camera, and a standard CCD camera confirm the model. The results open the field of quantum optical sensing using conventional detectors.

Twisted photons: new quantum perspectives in high dimensions

Twisted photons can be used as alphabets to encode information beyond one bit per single photon. This ability offers great potential for quantum information tasks, as well as for the investigation of fundamental questions. In this review article, we give a brief overview of the theoretical differences between qubits and higher dimensional systems, qudits, in different quantum information scenarios. We then describe recent experimental developments in this field over the past three years. Finally, we summarize some important experimental and theoretical questions that might be beneficial to understand better in the near future.