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This dictionary defines terms employed in international agreements, national legislation and scholarly legal studies related to comparative and international environmental law and the emerging law of climate change. Each term also includes its pinyin translation in order to facilitate accessing the Mandarin variants of each term.

The intrinsic connection between the transverse photonic spin Hall effect (PSHE) and the Imbert–Fedorov shift has been well characterized. However, physical insights into the longitudinal photonic spin splitting associated with the Goos-Hänchen (GH) shift remain elusive. This paper aims to expand the theory of the PSHE generation mechanism from the transverse to the longitudinal case by examining the reflection of each spin component from an arbitrarily linearly polarized incident Gaussian beam on the air-dielectric interface. Unlike the transverse case, both spin-maintained and spin-flipped modes exhibit non-zero longitudinal displacements, with the latter being affected by the second-order expansion term of the Fresnel reflection coefficient with respect to the in-plane wave-vector component. Meanwhile, the polarization angle plays a crucial role in determining the longitudinal PSHE since each reflected total spin component is a coherent superposition of these two corresponding modes. Remarkably, the imaginary part of the relative permittivity of the dielectric significantly affects the symmetry of the longitudinal PSHE. Furthermore, the GH shift results from a superposition of individual spin states’ longitudinal displacements, taking into account their energy weights. By incorporating the corresponding extrinsic orbital angular momentum, we explore the generation mechanism of the symmetric/asymmetric longitudinal PSHE. The unified physical framework elucidating the longitudinal photonic spin splitting and GH shift provides a comprehensive understanding of the fundamental origin of the PSHE and beam shifts, paving the way for potential applications in spin-controlled nanophotonics.

The quantum teleportation of composite quantum states of a single photon encoded in both spin and orbital angular momentum is achieved, with a teleportation fidelity above the classical limit, by quantum non-demolition measurement assisted discrimination of the Bell states describing the entanglement of the two degrees of freedom. Quantum teleportation of two states of one photon In the process known as quantum teleportation, quantum information encoded in a quantum particle, for example a photon, is transferred from one place to the other without ever moving the photon. Although quantum teleportation has been demonstrated with a variety of different systems, all have so far been limited in one crucial aspect: they only allow teleporting one degree of freedom. Here, Nai-Le Liu and colleagues demonstrate quantum teleportation of two degrees of freedom — spin and orbital angular momentum — in a single photon. Their experimental implementation is very complex and entails various innovative techniques, most notably a hybrid Bell-state measurement scheme. The intricacy of this scheme illustrates how difficult it will be to implement quantum teleportation of more complex quantum systems with more degrees of freedom. But this work represents a first and significant step in this direction. Quantum teleportation 1 provides a ‘disembodied’ way to transfer quantum states from one object to another at a distant location, assisted by previously shared entangled states and a classical communication channel. As well as being of fundamental interest, teleportation has been recognized as an important element in long-distance quantum communication 2 , distributed quantum networks 3 and measurement-based quantum computation 4 , 5 . There have been numerous demonstrations of teleportation in different physical systems such as photons 6 , 7 , 8 , atoms 9 , ions 10 , 11 , electrons 12 and superconducting circuits 13 . All the previous experiments were limited to the teleportation of one degree of freedom only. However, a single quantum particle can naturally possess various degrees of freedom—internal and external—and with coherent coupling among them. A fundamental open challenge is to teleport multiple degrees of freedom simultaneously, which is necessary to describe a quantum particle fully and, therefore, to teleport it intact. Here we demonstrate quantum teleportation of the composite quantum states of a single photon encoded in both spin and orbital angular momentum. We use photon pairs entangled in both degrees of freedom (that is, hyper-entangled) as the quantum channel for teleportation, and develop a method to project and discriminate hyper-entangled Bell states by exploiting probabilistic quantum non-demolition measurement, which can be extended to more degrees of freedom. We verify the teleportation for both spin–orbit product states and hybrid entangled states, and achieve a teleportation fidelity ranging from 0.57 to 0.68, above the classical limit. Our work is a step towards the teleportation of more complex quantum systems, and demonstrates an increase in our technical control of scalable quantum technologies.

Structured light has profoundly advanced optical manipulation, processing and imaging. However, its practical deployment in free space is limited by the constrained solutions of Helmholtz equation, which are bound to fixed propagation laws. Here, we reframe structured light as optical flows through a hydrodynamic description beyond the conventional field formalism, achieving flexible light structuring in free space via streamline engineering. Within this framework, we demonstrate the on-demand generation of diverse families of beams, with tailored propagation dynamics, including Gaussian, Bessel, Airy and vortex beams, and introduce specialized modes that overcome complex propagation challenges. To validate the designed energy streamlines, we perform optical tweezers experiments, treated as analogous to fluid particle-tracking velocimetry, demonstrating potential for high-precision optofluidic manipulation. For free-space optical communication, we show how vortex modes with a tailored flow can improve channel capacity, resilience to turbulence and non-line-of-sight capability. The hydrodynamic framework reported here provides precise control over light in free space, opening avenues in optomechanics, optofluidics, imaging, metrology, and communications. The propagation of structured light in free space is bound to the existing solutions of Helmholtz equation. Here, authors propose a hydrodynamic formulation of optics to design and generate well-known beam families and introduce additional specialized modes. The formalism is experimentally validated through optical tweezers and free-space communications.

We experimentally demonstrate that when three single photons transmit through two polarization channels, in a well-defined preand postselected ensemble, there are no two photons in the same polarization channel by weak-strength measurement, a counter-intuitive quantum counting effect called the quantum pigeonhole paradox. We further show that this effect breaks down in secondorder measurement. These results indicate the existence of the quantum pigeonhole paradox and its operating regime.

Structured beams endowed with topological charges and singularities show great potential for both classical and quantum information encoding. While manipulation of topological charges is well-established, information carriers based on topological invariants governing singularity evolution—optical links and knots—remain underexplored. The fundamental limitation lies in detection bandwidth: resolving singularities behaving like optical darkness through conventional intensity localization demands prohibitive exposure times, thereby constraining the transmission rates. To address this issue, we introduce a neuromorphic approach—Logarithmic Intensity Gradient Handling Technology for Event-based Links-and-knots Formation (LightELF)—which enables microsecond-level asynchronous spatial readout of sparse singularities. By fusing logarithmic gradient sampling with the superoscillating nature of singularities, LightELF reconstructs links and knots without post-processing while achieving orders-of-magnitude data reduction. Moreover, we demonstrate a topological binary signal processing chain integrating a high-throughput transmitter with our neuromorphic detector. This work establishes optical links and knots as viable information carriers, pioneering event sensing in topological photonics and providing a neuromorphic signal framework for optical information processing.

Quantum information masking (QIM) allows encoding quantum information in multipartite systems. Complete QIM is of great significance in quantum foundation and application. However, the realization of complete QIM, even for single-qubit encoded information, is still lacking. Here, we propose to demonstrate complete QIM with 4-qubit entangled states. The proposed QIM can be readily extended to multipartite systems with arbitrary number of subsystems, enabling quantum secret sharing (QSS) and quantum teleportation between multiplayers. In experiment, we build up a 4-qubit hyperentangled state to implement complete QIM. The trace distance of 16 encoded single-qubit states falls within the range of 0.12 ± 0.02 to 0.03 ± 0.02. Furthermore, we implement QSS between six players by expanding the 4-qubit state to a 6-qubit state entangled in hybrid manner, in which we observe an average fidelity 0.85 ± 0.03 of the recovered states. Our results open the door towards QIM-enabled quantum information processing and provide applications in quantum communications. Quantum information masking allows encoding quantum information in multipartite systems, which is hidden from subsystems and can be recovered from the nonlocal correlation. The authors propose and realize the complete quantum information masking and apply it to quantum secret sharing between six players.

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.

Orbital angular momentum (OAM) of photons, as a new fundamental degree of freedom, has excited a great diversity of interest, because of a variety of emerging applications. Arbitrarily tunable OAM has gained much attention, but its creation remains still a tremendous challenge. We demonstrate the realization of well-controlled arbitrarily tunable OAM in both theory and experiment. We present the concept of general OAM, which extends the OAM carried by the scalar vortex field to the OAM carried by the azimuthally varying polarized vector field. The arbitrarily tunable OAM we presented has the same characteristics as the well-defined integer OAM: intrinsic OAM, uniform local OAM and intensity ring and propagation stability. The arbitrarily tunable OAM has unique natures: it is allowed to be flexibly tailored and the radius of the focusing ring can have various choices for a desired OAM, which are of great significance to the benefit of surprising applications of the arbitrary OAM.

Particle-laden turbulent flows over a backward-facing step were here numerically studied by means of a large-eddy simulation considering two-way coupling between particle and fluid phases. The modification of turbulence by particles was then analyzed based on the predicted results of mean and fluctuating velocities. The influencing factors of particle size and material density were also evaluated. Turbulence modifications are anisotropic and closely dependent on flow status. Stronger modulations were observed in the up-wall shear flow regions. Fluid laden with smaller size, low-density particles showed enhancement of turbulence in the streamwise direction, but this effect was less pronounced in the case of larger low-density particles. Particle dispersions were also investigated for comparison of particle instantaneous distributions in coherent structures. Particle modulations of turbulence were not found to change particle preferential distributions. The conclusions drawn in the present study were useful for further understanding of a two-phase turbulence physical mechanism and establishment of accurate prediction models for engineering applications.