Spatial Degrees Of Freedom Research Articles

Remote implementation of hidden or partially unknown quantum operators using optimal resources: a generalized view

Two protocols are proposed for two closely linked but different variants of remote implementation of quantum operators of specific forms The first protocol is designed for the remote implementation of the single qubit hidden quantum operator, whereas the second one is designed for the remote implementation of the partially unknown single qubit quantum operator. In both cases two-qubit maximally entangled state, which is entangled in the spatial degree of freedom is used. The quantum resources used here are optimal and easy to realize and maintain in comparison to the multi-partite or multi-mode entangled states used in earlier works. The impact of photon loss due to interaction with the environment is analyzed for both the schemes. The proposed protocols are also generalized to their controlled, bidirectional, cyclic, controlled cyclic, and controlled bidirectional versions and it is shown that either Bell state alone or products of Bell states will be sufficient to perform these tasks with some additional classical communications in the controlled cases only. This is in sharp contrast to the earlier proposals that require large entangled states. In addition, it’s noted that remote implementation of hidden or partially unknown operators involving multiple controllers and/or multiple players who jointly apply the desired operator(s) would require quantum channels more complex than the Bell states and their products. Explicit forms of such quantum channels are also provided.

Improved Entanglement‐Based High‐Dimensional Optical Quantum Computation with Linear Optics

AbstractQuantum gates are the essential block for quantum computers. High‐dimensional quantum gates exhibit remarkable advantages over their 2D counterparts for some quantum information processing tasks. Here, a family of entanglement‐based optical controlled‐SWAP gates on is presented. With the hybrid encoding, the control qubits and target qudits are encoded in photonic polarization and spatial degrees of freedom, respectively. The circuit is constructed using only () linear optics, beating an earlier result of 14 linear optics with . The circuit depth five is much lower than an earlier result of 11 with . Besides, the fidelity of the presented circuit can reach 99.4%, and it is higher than the previous counterpart with . The scheme is constructed in a deterministic way without any borrowed ancillary photons or measurement‐induced nonlinearities. Moreover, the approach allows .

Research on an Active Adjustment Mechanism Based on Non-Singular Terminal Sliding Mode and Finite-Time Disturbance Observer

With the continuous development of synchrotron radiation light sources, higher requirements have been put forward for the stability of double-crystal monochromators in synchrotron radiation facilities. This paper designs an active adjustment mechanism for a double-crystal monochromator to improve its stability. Firstly, three spatial degrees of freedom are designed based on the active adjustment mechanism of flexible leaf spring parallel coupling, and the prototype of the mechanism is fabricated. Secondly, system identification experiments are carried out and the system transfer function curve is fitted by the nonlinear least squares method. Thirdly, the controller based on non-singular terminal sliding modes and a finite-time disturbance observer was designed for stability control and disturbance compensation. Finally, the effectiveness of the controller is verified by a model-in-the-loop approach based on the performance of the real-time target machine. The results show that the non-singular terminal sliding mode + finite-time disturbance observer control strategy can reduce the RMS value of the vibration displacement of Axis-1/Axis-2/Axis-3 by 81.25%, 78.53%, and 71.82%.

Hybrid Beam-Forming Techniques for 6G Terahertz Communication: Challenges

The terahertz band is the main pillar of 6G wireless communication system. It is difficult to meet the high data rate of 1Tbps by millimeter frequency support systems. The terahertz band suffers huge propagation loss limiting wireless distance. Terahertz band imposes ultra massive multiple input multiple output antenna (UM-MIMO) systems which produce high array gain with narrow beamforming. The conventional methods for MIMO beamforming are Analog and Digital beamforming. The fully digital beamforming methods utilize dedicated structure of DAC/ADC and RF chains. These structures increase hardware complexity and are power hungry. The analog beamforming structures utilize ADC/DAC with phase shifters with less hardware complexity but support less data rates. As a result, a hybrid beamforming method can be adapted for UM-MIMO systems. This paper investigates challenges in hybrid beamforming architecture which will address the low spatial degrees of freedom (SDoF) limitation in Terahertz (THz) Communication. The flexible hardware connections are proposed, in order to switch the system in an adaptive manner so as to minimize the power requirements.

Universality of quantum time dilation

Time dilation is a difference in measured time between two clocks that either move with different velocities or experience different gravitational potentials. Both of these effects stem from the theory of relativity and are usually associated with classically defined trajectories, characterized by position, momentum, and acceleration. However, when spatial degrees of freedom are treated in a quantum way and a clock is allowed to be in a coherent superposition of either two momenta or two heights, additional quantum corrections to classical time dilation appear, called kinematic and gravitational quantum time dilations, respectively. We show that similarly to its classical counterpart, kinematic quantum time dilation is universal for any clock mechanism, while gravitational quantum time dilation is not. We also show that although both of these effects reduce to incoherent averaging of different classical time dilation contributions, there exists an additional quantum time dilation effect that has no classical analog and can be extracted from higher-order corrections to the system’s Hamiltonian.

Reservoir-Free Decoherence in Flying Qubits.

An effective time-dependent Hamiltonian can be implemented by making a quantum system fly through an inhomogeneous potential, realizing, for example, a quantum gate on its internal degrees of freedom. However, flying systems have a spatial spread that will generically entangle the internal and spatial degrees of freedom, leading to decoherence in the internal state dynamics, even in the absence of any external reservoir. We provide formulas valid at all times for the dynamics, fidelity, and change of entropy for ballistic particles with small spatial spreads, quantified by Δx. This non-Markovian decoherence can be significant for ballistic flying qubits (scaling as Δx^{2}) but usually not for flying qubits carried by a moving potential well (scaling as Δx^{6}). We also discuss a method to completely counteract this decoherence for a ballistic qubit later measured.

Measuring the Optical Concurrence of Vector Beams with an Atomic-State Interferometer

We investigate the transmission of vector beams, correlated in their polarization and spatial degrees of freedom, through cold atoms in the presence of a transverse magnetic coupling field. The resulting phase-dependent dynamics allow us to imprint the spatially varying polarization of a vector beam onto atomic spin polarizations, thereby establishing a direct link between optical space-polarization correlations and atomic-state interference. We find that the resulting absorption profiles show interference fringes whose modulation strength is given by the squared concurrence of the vector beam, letting us identify optical concurrence from a single absorption image. We expect impact across a diverse range of applications, including spintronics, quantum memories, metrology, and clocks. Published by the American Physical Society 2024

Two-photon absorption cross sections of pulsed entangled beams.

Entangled two-photon absorption (ETPA) could form the basis of nonlinear quantum spectroscopy at very low photon fluxes, since, at sufficiently low photon fluxes, ETPA scales linearly with the photon flux. When different pairs start to overlap temporally, accidental coincidences are thought to give rise to a "classical" quadratic scaling that dominates the signal at large photon fluxes and, thus, recovers a supposedly classical regime, where any quantum advantage is thought to be lost. Here, we scrutinize this assumption and demonstrate that quantum-enhanced absorption cross sections can persist even for very large photon numbers. To this end, we use a minimal model for quantum light, which can interpolate continuously between the entangled pair and a high-photon-flux limit, to analytically derive ETPA cross sections and the intensity crossover regime. We investigate the interplay between spectral and spatial degrees of freedom and how linewidth broadening of the sample impacts the experimentally achievable enhancement.

Bloch oscillations, Landau–Zener transition, and topological phase evolution in an array of coupled pendula

We experimentally and theoretically study the dynamics of a one-dimensional array of pendula with a mild spatial gradient in their self-frequency and where neighboring pendula are connected with weak and alternating coupling. We map their dynamics to the topological Su-Schrieffer-Heeger model of charged quantum particles on a lattice with alternating hopping rates in an external electric field. By directly tracking the dynamics of a wave-packet in the bulk of the lattice, we observe Bloch oscillations, Landau-Zener transitions, and coupling between the isospin (i.e., the inner wave function distribution within the unit cell) and the spatial degrees of freedom (the distribution between unit cells). We then use Bloch oscillations in the bulk to directly measure the nontrivial global topological phase winding and local geometric phase of the band. We measure an overall evolution of 3.1 [Formula: see text] 0.2 radians for the geometrical phase during the Bloch period, consistent with the expected Zak phase of [Formula: see text]. Our results demonstrate the power of classical analogs of quantum models to directly observe the topological properties of the band structure and shed light on the similarities and the differences between quantum and classical topological effects.

Directional synchrony among self-propelled particles under spatial influence.

Synchronization is one of the emerging collective phenomena in interacting particle systems. Its ubiquitous presence in nature, science, and technology has fascinated the scientific community over the decades. Moreover, a great deal of research has been, and is still being, devoted to understand various physical aspects of the subject. In particular, the study of interacting active particles has led to exotic phase transitions in such systems which have opened up a new research front-line. Motivated by this line of work, in this paper, we study the directional synchrony among self-propelled particles. These particles move inside a bounded region, and crucially their directions are also coupled with spatial degrees of freedom. We assume that the directional coupling between two particles is influenced by the relative spatial distance which changes over time. Furthermore, the nature of the influence is considered to be both short and long-ranged. We explore the phase transition scenario in both the cases and propose an approximation technique which enables us to analytically find the critical transition point. The results are further supported with numerical simulations. Our results have potential importance in the study of active systems like bird flocks, fish schools, and swarming robots where spatial influence plays a pertinent role.

Quantum transport of high-dimensional spatial information with a nonlinear detector

Information exchange between two distant parties, where information is shared without physically transporting it, is a crucial resource in future quantum networks. Doing so with high-dimensional states offers the promise of higher information capacity and improved resilience to noise, but progress to date has been limited. Here we demonstrate how a nonlinear parametric process allows for arbitrary high-dimensional state projections in the spatial degree of freedom, where a strong coherent field enhances the probability of the process. This allows us to experimentally realise quantum transport of high-dimensional spatial information facilitated by a quantum channel with a single entangled pair and a nonlinear spatial mode detector. Using sum frequency generation we upconvert one of the photons from an entangled pair resulting in high-dimensional spatial information transported to the other. We realise a d = 15 quantum channel for arbitrary photonic spatial modes which we demonstrate by faithfully transferring information encoded into orbital angular momentum, Hermite-Gaussian and arbitrary spatial mode superpositions, without requiring knowledge of the state to be sent. Our demonstration merges the nascent fields of nonlinear control of structured light with quantum processes, offering a new approach to harnessing high-dimensional quantum states, and may be extended to other degrees of freedom too.

Tetraquark mass relations in quark and diquark models

We present new linear relations among the masses of S-wave tetraquarks with either one flavour (QQQ¯Q¯) or two (QQq¯q¯). Because the relations are sensitive to the hidden-colour, spin, and spatial degrees of freedom, comparison to experimental data can help to reveal the internal structure of tetraquarks, and discriminate among different theoretical models. Depending on the model, the relations are either exact, or valid in perturbation theory, and a thorough comparison with existing literature confirms their validity at the MeV level. Additionally, we explore the connections among tetraquark models, and show how those with effective (quark or diquark) masses are related to dynamical potential models. We also show how the spectrum of diquark models is effectively a limiting case of (more general) quark models, and in particular, that the diquark concept is most relevant in the particular combination QQq¯q¯, where Q is much heavier than q¯.

Helico-conical vector beams.

In this work, we propose and demonstrate experimentally a new family of vector beams, the helico-conical vector beams (HCVBs), whose spatial degree of freedom is encoded in the helico-conical optical beams. We use Stokes polarimetry to study their properties and find that upon propagation their transverse polarization distribution evolves from nonhomogeneous to quasihomogeneous, such that even though their global degree of nonseparability remains constant, locally it decreases to a minimum value as z → ∞. We corroborated this quantitatively using the Hellinger distance, a novel metric for vectorness that applies to spatially disjoint vector modes. To the best of our knowledge, HCVBs are the second family of vector beams featuring this behavior, paving the way for applications in optical tweezing or information encryption.

Time-dependent variational approach to solve multi-dimensional time-dependent Schrödinger equation

We present an efficient approach to solve multi-dimensional time-dependent Schrödinger equation (TDSE) in an intense laser field. In this approach, each spatial degree of freedom is treated as a distinguishable quasi-particle. The non-separable Coulomb potential is regarded as a two-body operator between different quasi-particles. The time-dependent variational principle is used to derive the equations of motion. Then the high-order multi-dimensional problem is broken down into several lower-order coupled equations, which can be efficiently solved. As a demonstration, we apply this method to solve the two-dimensional TDSE. The accuracy is tested by comparing the direct solutions of TDSE using several examples such as the strong-field ionization and the high harmonic generation. The results show that the present method is much more computationally efficient than the conventional one without sacrificing accuracy. The present method can be straightforwardly extended to three-dimensional problems. Our study provides a flexible method to investigate the laser-atom interaction in the nonperturbative regime.

Spatial Channel Degrees of Freedom for Optimum Antenna Arrays

One of the ultimate goals of future wireless networks is to maximize data rates to accommodate bandwidth-hungry services and applications. Thus, extracting the maximum amount of information bits for given spatial constraints when designing wireless systems will be of great importance. In this paper, we present antenna array topologies that maximize the communication channel capacity for given number of array elements while occupying minimum space. Capacity is maximized via the development of an advanced particle swarm optimization (PSO) algorithm devising optimum standardized and arbitrarily-shaped antenna array topologies. Number of array elements and occupied space are informed by novel heuristic spatial degrees of freedom (SDoF) formulations which rigorously generalize existing SDoF formulas. Our generalized SDoF formulations rely on the differential entropy of three-dimensional (3D) angle of arrival (AOA) distributions and can associate the number of array elements and occupied space for any AOA distribution. The proposed analysis departs from novel closed-form spatial correlation functions (SCFs) of arbitrarily-positioned array elements for all classes of 3D multipath propagation channels, namely, isotropic, omnidirectional, and directional. Extensive simulation runs and comparisons with existing trivial solutions verify correctness of our SDoF formulations resulting in optimum antenna array topologies with maximum capacity performance and minimum space occupancy.

Deterministic Hyperparallel Control Gates with Weak Kerr Effects

AbstractBy harnessing weak cross‐Kerr nonlinearities, it proposes two deterministic hyperparallel quantum control gates, including the hyperparallel controlled‐NOT (hyper‐CNOT) gate and hyperparallel Fredkin (hyper‐Fredkin) gate for photonic systems in the polarization and spatial degrees of freedom (DoFs), which are composed of two procedures for the implementations of the first polarized control (CNOT and Fredkin) gates and the second spatial control (CNOT and Fredkin) ones in turn. Moreover, compared with the two two‐photon CNOT gates (three‐photon Fredkin gates) in one DoF, the hyper‐CNOT (hyper‐Fredkin) gate is provided with more straightforward quantum circuits, lower computational costs of resource overhead (without the assistance of single photons or entangled states), less cross‐Kerr nonlinear interactions between three photons and the coherent states, and reduces the effect caused by photon‐loss noise. The success probabilities of two quantum control gates are approximated unit by performing the corresponding classical feed‐forward operations based on the different measuring outcomes of the X‐homodyne detectors to be aimed at the coherent states, and they are robust against the photon loss as well, which are feasible with the current technology and convenient in practical applications.

Beamspace Modulation for Near Field Capacity Improvement in XL-MIMO Communications

The spatial degrees of freedom (DoFs) greatly increase in the near-field region of millimeter wave or terahertz multiple-input multiple-output communications with extremely large antenna arrays (XL-MIMO). To employ the increased spatial DoFs, a beamspace modulation (BM) strategy is introduced to the near field of XL-MIMO. BM can work with a fixed small number of RF chains. It exploits the increased spatial DoFs as modulation resources for capacity improvements. The achievable spectral efficiency and its asymptotic capacity are analyzed. Both theoretical and simulation results show that the proposed BM strategy considerably outperforms the existing benchmark that only selects the best beamspace for data transmission in terms of spectral efficiency.

Hyper-entangling mesoscopic bound states

We predict hyper-entanglement generation by binary scattering of mesoscopic bound states, considering solitary waves in Bose–Einstein condensates containing thousands of identical Bosons. For it to occur, the underlying many-body Hamiltonian must not be integrable, and the pre-collision quantum state of the solitons needs to be fragmented. Under these conditions, we show that the post-collision state will be hyper-entangled in spatial degrees of freedom and atom number within solitons, for realistic parameters. The effect links aspects of non-linear systems and quantum-coherence and the entangled post-collision state challenges present entanglement criteria for identical particles. Our results are based on simulations of colliding quantum solitons in a quintic interaction model beyond the mean-field, using the truncated Wigner approximation.

Generating indistinguishability within identical particle systems: spatial deformations as quantum resource activators.

Identical quantum subsystems can possess a property which does not have any classical counterpart: indistinguishability. As a long-debated phenomenon, identical particles' indistinguishability has been shown to be at the heart of various fundamental physical results. When concerned with the spatial degree of freedom, identical constituents can be made indistinguishable by overlapping their spatial wave functions via appropriately defined spatial deformations. By the laws of quantum mechanics, any measurement designed to resolve a quantity which depends on the spatial degree of freedom only and performed on the regions of overlap is not able to assign the measured outcome to one specific particle within the system. The result is an entangled state where the measured property is shared between the identical constituents. In this work, we present a coherent formalization of the concept of deformation in a general [Formula: see text]-particle scenario, together with a suitable measure of the degree of indistinguishability. We highlight the basic differences with non-identical particles scenarios and discuss the inherent role of spatial deformations as entanglement activators within the spatially localized operations and classical communication operational framework. This article is part of the theme issue 'Identity, individuality and indistinguishability in physics and mathematics'.

A Tutorial on Holographic MIMO Communications—Part II: Performance Analysis and Holographic Beamforming

As Part II of a three-part tutorial on holographic multiple-input multiple-output (HMIMO), this Letter focuses on the state-of-the-art in performance analysis and on holographic beamforming for HMIMO communications. We commence by discussing the spatial degrees of freedom (DoF) and ergodic capacity of a point-to-point HMIMO system, based on the channel model presented in Part I. Additionally, we also consider the sum-rate analysis of multi-user HMIMO systems. Moreover, we review the recent progress in holographic beamforming techniques developed for various HMIMO scenarios. Finally, we evaluate both the spatial DoF and the channel capacity through numerical simulations.