Entanglement transfer, accumulation and retrieval via quantum-walk-based qubit–qudit dynamics

Optical networks implementing single-qudit quantum computation gates may\nexhibit superior properties to those for qubits as each of the optical elements\nin the network can work in parallel on many optical modes simultaneously. We\npresent an important class of such networks, that implements in a deterministic\nand efficient way the quantum Fourier transform (QFT) in an arbitrarily large\ndimension. These networks redistribute the initial quantum state into the path\nand orbital angular momentum (OAM) degrees of freedom and exhibit two modes of\noperation. Either the OAM-only QFT can be implemented, which uses the path as\nan internal auxiliary degree of freedom, or the path-only QFT is implemented,\nwhich uses the OAM as the auxiliary degree of freedom. The resources for both\nschemes scale linearly $O(d)$ with the dimension $d$ of the system, beating the\nbest known bounds for the path-encoded QFT. While the QFT of the orbital\nangular momentum states of single photons has been applied in a multitude of\nexperiments, these schemes require specially designed elements with non-trivial\nphase profiles. In contrast, we present a different approach that utilizes only\nconventional optical elements.\n

We study the topic of non-linear light-matter interaction for the generation of multi-photon entangled states. In particular, we want the quantum correlations to be inherent in the Orbital Angular Momentum (OAM) degree of freedom. Our first proposal is to generate four photons, multidimensional, spatially-entangled states, while the final goal is to make them interact with nanostructures for quantum metrology applications.

An atmospheric imaging system based on quantum hyper-entanglement has been developed. Hyper-entanglement refers to entanglement in more than one degree of freedom, e.g. polarization, energy-time and orbital angular momentum (OAM). The system functions at optical or infrared frequencies. Only the signal photon propagates in the atmosphere, the ancilla photon is retained within the detector. This results in loss being essentially classical, giving rise to stronger forms of entanglement. Bell state generation and Bell state measurement, i.e. the ability to distinguish the various Bell states is discussed. A mathematical representation of Bell state generation and the Bell state analyzer, including a projection operator describing the measurement process is provided. Signatures for unique detection of the various Bell states are developed. A method and design for creating states hyper-entangled in polarization, energy-time, OAM and the radial quantum number is examined. Hermite-Gaussian (HG) modes, Laguerre-Gaussian (LG) modes, OAM dependence of the LG modes and a method of mode conversion are discussed. A projection operator that represents the combined measurements between the different degrees of freedom is provided. A model of generation and detection efficiencies for the different degrees of freedom and the implications for signal to noise ratio (SNR), signal to interference ratio (SIR), the quantum Cramer-Rao lower bound, and the measurement time are provided in closed form. A formula describing how hyper-entanglement greatly improves the maximum detection range of the system is derived. The formalism permits random noise and entangled or non-entangled sources of interference to be modeled.

Quantum information science has leaped forward with the exploration of high-dimensional quantum systems, offering greater potential than traditional qubits in quantum communication and quantum computing. To advance the field of high-dimensional quantum technology, a significant effort is underway to progressively enhance the entanglement dimension between two particles. An alternative effective strategy involves not only increasing the dimensionality but also expanding the number of particles that are entangled. We present an experimental study demonstrating multi-partite quantum non-locality beyond qubit constraints, thus moving into the realm of strongly entangled high-dimensional multi-particle quantum systems. In the experiment, quantum states were encoded in the path degree of freedom (DoF) and controlled via polarization, enabling efficient operations in a two-dimensional plane to prepare three- and four-particle Greenberger-Horne-Zeilinger (GHZ) states in three-level systems. Our experimental results reveal ways in which high-dimensional systems can surpass qubits in terms of violating local-hidden-variable theories. Our realization of multiple complex and high-quality entanglement technologies is an important primary step for more complex quantum computing and communication protocols.

High-dimensional entanglement is a key resource for quantum cryptography. We experimentally realise the criterion for secure quantum key distribution when using photons entangled in the orbital angular momentum and angle degrees of freedom.

The polarization and orbital angular momentum (OAM) degrees of freedom carried by light have important applications in precision optical measurement and optical sensing. Here we show that the electro-optic Pockels effect of a magnesium-doped lithium niobate (MgO:LiNbO3) crystal can be used to measure a low-frequency electric field. By exploiting the rotation property of superposition OAM light, we experimentally observe that the minimum measured precision of electric field intensity is about 0.18 V/m. This study offers a method to perform low-frequency electric field sensing.

A combination of orbital angular momentum (OAM) and spin angular momentum (SAM) degrees of freedom for a single photon leads to enhanced transmission rates and security in high-dimensional quantum key distribution (QKD) systems. Therefore, the actual commercial QKD sources require accurate and fast generation of encoded states. This paper proposes a schemed and numerically verified integrated high-speed and low-loss electro-optical modulator for the manipulation of modes encoded in OAM-SAM states. The modulator is designed as an electro-optically active lithium niobate on insulator photonic wire configuration. The obtained results indicate the high purity (>92%) and low quantum bit error rate (∼8%) generation of encoded states for 4D-QKD with structured photons via low applied voltage values not more than 9 volts.

Light orbital angular momentum (OAM) has been recognized as a new promising resource for classical and quantum information applications. In contrast to the spin angular momentum, the OAM is an inherently multidimensional. Thus, the information can be encoded in the higher-dimensional OAM alphabets. Recently, Marrucci et al. have invented a new device named q-plate (QP), made of liquid crystal cell patterned in such a way to introduce a topological charge q at the transverse plane, which is able to generate a well-defined values of photon OAM. My research has been aimed at investigating the physics of the QP, of the optical fields that it generates and of its possible applications for optical communication and quantum information. We studied both theoretically and experimentally a novel set of non-orthogonal but over-complete paraxial modes, named Hypergeometric-Gaussian modes, that is typically associated with OAM-carrying optical fields. We have also found the light propagation kernel inside the QP and we have shown analytically that if small losses due to reflection, absorption, and scattering are neglected, the QP can convert the photon spin into OAM with up to 100 \% efficiency. We implemented a technique to control the QP optical retardation by tuning the QP temperature. At the optimal temperature, the QP can generate a beam with up to 97\% efficiency. Moreover, the OAM state generated by QP can be rotated easily in the 2D OAM Hilbert space by proper manipulation of the input polarization state, a fact which opens a new way of beam shape controlling in MHz scale. We also performed a novel way to encode and read two bits information on the 4D OAM space by using only one QP. Finally, we experimentally demonstrated the transfer of quantum information from spin to OAM and vice versa, including the case of bi-photon states having quantum correlations. Furthermore, by exploiting these quantum information transfer devices, we demonstrated the Hong-Ou-Mandel effect and the optimal quantum cloning with OAM-carrying photons.

The capability to engineer and characterize high dimensional states has become a crucial request in the quantum information field. The quantum walk dynamics proved to be a suitable resource for developing general quantumstate engineering protocols. Here, we experimentally verified the flexibility of an engineering protocol based on a one-dimensional quantum walk in the Orbital Angular Momentum (OAM). Although this degree of freedom has found several applications in the quantum information field, extract the information stored in them appears to be difficult. Therefore, we employ machine learning protocols to classify and characterize particularly structured beams endowed with a not uniform distribution of the polarization on the transverse plane. Moreover, we prove that by modeling the engineering process through a refined model it is possible to improve the performances of measurement techniques such as holographic projection and machine-learning based classification. These results represent a further investigation in the manipulation and detection of OAM modes coupling the photonics platforms with machine-learning protocols.

Photon is an ideal carrier of quantum information, which can carry spin angular momentum and orbital angular momentum. In recent years, orbital angular momentum has shown great application prospects in quantum communication, quantum radar and other fields. It has gradually become a research hotspot in the field of detection. It is necessary to calibrate and measure the orbital angular momentum before it is applied to the detection field. Based on the interference principle and aperture diffraction theory, the measurement of orbital angular momentum is realized indirectly, and the experimental platform is built to verify part of the simulation results. It provides technical support for the subsequent implementation of quantum detection technology.

The capability to generate and manipulate quantum states in high-dimensional Hilbert spaces is a crucial step for the development of quantum technologies, from quantum communication to quantum computation. One-dimensional quantum walk dynamics represents a valid tool in the task of engineering arbitrary quantum states. Here we affirm such potential in a linear-optics platform that realizes discrete-time quantum walks in the orbital angular momentum degree of freedom of photons. Different classes of relevant qudit states in a six-dimensional space are prepared and measured, confirming the feasibility of the protocol. Our results represent a further investigation of quantum walk dynamics in photonics platforms, paving the way for the use of such a quantum state-engineering toolbox for a large range of applications.

Quantum information, communication, and sensing rely on the generation and control of quantum correlations in complementary degrees of freedom. Free electrons coupled to photonics promise novel hybrid quantum technologies, although single-particle correlations and entanglement have yet to be shown. In this work, we demonstrate the preparation of electron-photon pair states using the phase-matched interaction of free electrons with the evanescent vacuum field of a photonic chip-based optical microresonator. Spontaneous inelastic scattering produces intracavity photons coincident with energy-shifted electrons, which we employ for noise-suppressed optical mode imaging. This parametric pair-state preparation will underpin the future development of free-electron quantum optics, providing a route to quantum-enhanced imaging, electron-photon entanglement, and heralded single-electron and Fock-state photon sources.

In addition to spin angular momentum, light can carry orbital angular momentum. The orbital angular momentum degree of freedom in the extreme ultraviolet and x-ray regimes enables fundamental studies of light–matter interactions and new methods to study materials. Advances in x-ray optics, as well as undulator radiation and high harmonic generation techniques, lead to the creation of beams with non-trivial phase structure, such as a helical phase structure, creating new possibilities for the use of extreme ultraviolet and x-ray photons with orbital angular momentum in probing complex electronic structures in matter. In this article, we review the generation and applications of orbital angular momentum beams in the x-ray and extreme ultraviolet regime. We discuss several recent works that exploit the orbital angular momentum degree of freedom and showcase the potential advantages of using these beams.

Opposite directionality of the Poynting vector and the wave vector, an inherent property of negative index metamaterials (NIMs), was predicted to enable backward phase-matching condition for a second harmonic generation (SHG) process. As a result, such a nonlinear negative index slab acts as a nonlinear mirror. In this Letter, we predict that SHG with structured light carrying orbital angular momentum (OAM) and propagating in NIMs results in a possibility of generating a backward propagating beam with simultaneously doubled frequency, OAM, and reversed rotation direction of the wavefront. These results may find applications in high-dimensional communication systems, quantum information processing, and optical manipulation on a nanoscale.

The identification of orbital angular momentum (OAM) as a fundamental property of a beam of light nearly 25 years ago has led to an extensive body of research around this topic. The possibility that single photons can carry OAM has made this degree of freedom an ideal candidate for the investigation of complex quantum phenomena and their applications. Research in this direction has ranged from experiments on complex forms of quantum entanglement to the interaction between light and quantum states of matter. Furthermore, the use of OAM in quantum information has generated a lot of excitement, as it allows for encoding large amounts of information on a single photon. Here, we explain the intuition that led to the first quantum experiment with OAM 15 years ago. We continue by reviewing some key experiments investigating fundamental questions on photonic OAM and the first steps to applying these properties in novel quantum protocols. At the end, we identify several interesting open questions that could form the subject of future investigations with OAM.This article is part of the themed issue 'Optical orbital angular momentum'.