High-dimensional Quantum Research Articles

Realization of a Multi-Output Quantum Pulse Gate for Decoding High-Dimensional Temporal Modes of Single-Photon States

Temporal modes (TMs) of photons provide an appealing high-dimensional encoding basis for quantum information. While techniques to generate TM states have been established, high-dimensional decoding of single-photon TMs remains an open challenge. In this work, we experimentally demonstrate demultiplexing of five-dimensional TMs of single photons with an average fidelity of 0.96±0.01, characterized via measurement tomography. This is achieved with use of a newly developed device, the multi-output quantum pulse gate (MQPG). We demonstrate a proof-of-principle complete decoder based on the MQPG that operates on any basis from a set of six five-dimensional mutually unbiased bases and is therefore suitable as a receiver for high-dimensional quantum key distribution. Furthermore, we confirm the high-quality operation of the MQPG by performing resource-efficient state tomography with an average fidelity of 0.98±0.02.3 MoreReceived 20 September 2022Accepted 15 March 2023DOI:https://doi.org/10.1103/PRXQuantum.4.020306Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasIntegrated opticsNonlinear waveguidesOptical quantum information processingQuantum communicationQuantum gatesQuantum opticsQuantum tomographyQuantum Information

FPGA based hardware platform for trapped-ion-based multi-level quantum systems

We report a design and implementation of a field-programmable-gate-arrays (FPGA) based hardware platform, which is used to realize control and signal readout of trapped-ion-based multi-level quantum systems. This platform integrates a four-channel 2.8 Gsps@14 bits arbitrary waveform generator, a 16-channel 1 Gsps@14 bits direct-digital-synthesis-based radio-frequency generator, a 16-channel 8 ns resolution pulse generator, a 10-channel 16 bits digital-to-analog-converter module, and a 2-channel proportion integration differentiation controller. The hardware platform can be applied in the trapped-ion-based multi-level quantum systems, enabling quantum control of multi-level quantum system and high-dimensional quantum simulation. The platform is scalable and more channels for control and signal readout can be implemented by utilizing more parallel duplications of the hardware. The hardware platform also has a bright future to be applied in scaled trapped-ion-based quantum systems.

Orbital Angular Momentum in Fibers

Orbital angular momentum (OAM) of light beams with helical phase front, as an alternative spatial dimension resource of photons, has attracted extensive attention over the past decades. Very recently, OAM in fibers has facilitated rapid development of various fiber-based applications, such as optical communications, optical manipulation, optical sensing, optical imaging, nonlinear optics, and quantum science. Comprehensive and in-depth understanding of OAM in fibers is of great interest to researchers in this area. Here, we give a tutorial overview of OAM in fibers. We first introduce the basic theories, including the eigenmode analysis method, mode coupling theory, and spin-orbit mapping of light in fibers. We then give a detailed classification of OAM fibers and discuss versatile spatial mode bases in fibers. After that, we review various OAM fiber designs, including conventional single-mode fibers, conventional multi-mode fibers, ring-core fibers, air-core fibers, photonic crystal fibers, negative-curvature hollow-core fibers, multi-core fibers, active fibers (e.g., erbium-doped fibers), etc. Besides, we describe the state-of-the-art commercial fiber manufacturing processes as well as testing and characterization methods for OAM fibers. We also review various active and passive OAM fiber devices. Moreover, we introduce several typical advanced applications based on OAM fibers, such as capacity scaling fiber-optic communications, remote vectorial Doppler velocimetry, super-resolution optical imaging, and high-dimensional quantum cryptography. Finally, we briefly discuss future challenges and prospects of OAM in fibers.

Resource reduction in multiplexed high-dimensional quantum Reed-Solomon codes

Quantum communication technologies will play an important role in quantum information processing in the near future as we network devices together. However, their implementation is still a challenging task due to both loss and gate errors. Quantum error correction codes are one important technique to address this issue. In particular, the Quantum Reed-Solomon codes are known to be quite efficient for quantum communication tasks. The high degree of physical resources required, however, makes such a code difficult to use in practice. A recent technique called quantum multiplexing has been shown to reduce resources by using multiple degrees of freedom of a photon. In this work, we propose a method to decompose multi-controlled gates using fewer $\rm{CX}$ gates via this quantum multiplexing technique. We show that our method can significantly reduce the required number of $\rm{CX}$ gates needed in the encoding circuits for the quantum Reed-Solomon code. Our approach is also applicable to many other quantum error correction codes and quantum algorithms, including Grovers and quantum walks.

Continuous variable spin-orbit total angular momentum entanglement on the higher-order Poincaré sphere.

Optical spin-orbit coupling is an important phenomenon and has fruitful applications. Here, we investigate the spin-orbit total angular momentum entanglement in the optical parametric downconversion process. Four pairs of entangled vector vortex modes are experimentally generated directly using a dispersion- and astigmatism-compensated single optical parametric oscillator, and for the first time, to the best of our knowledge, the spin-orbit quantum states are characterized on the quantum higher-order Poincaré sphere, and the relationship of spin-orbit total angular momentum Stokes entanglement is demonstrated. These states have potential applications in high-dimensional quantum communication and multiparameter measurement.

Selectively gas-filled anti-resonant hollow-core fibers for broadband high-purity LP11 mode guidance.

An anti-resonant hollow-core fiber capable of propagating the LP11 mode with high purity and over a wide wavelength range is proposed and demonstrated. The suppression of the fundamental mode relies on the resonant coupling with specific gas selectively filled into the cladding tubes. After a length of 2.7 m, the fabricated fiber shows a mode extinction ratio of over 40 dB at 1550 nm and above 30 dB in a wavelength range of 150 nm. The loss of the LP11 mode is measured to be 2.46 dB/m at 1550 nm. We discuss the potential application of such fibers in high-fidelity high-dimensional quantum state transmission.

Solving the Wigner equation for chemically relevant scenarios: Dynamics in 2D.

The signed particle Monte Carlo (SPMC) approach has been used in the past to model steady-state and transient dynamics of the Wigner quasi-distribution for electrons in low-dimensional semiconductors. Here, we make a step toward high-dimensional quantum phase-space simulation in chemically relevant scenarios by improving the stability and memory demands of SPMC in 2D. We do so by using an unbiased propagator for SPMC to improve trajectory stability and applying machine learning to reduce memory demands for storage and manipulation of the Wigner potential. We perform computational experiments on a 2D double-well toy model of proton transfer and demonstrate stable pico-second-long trajectories that require only a modest computational effort.

Analytical high-dimensional operators in canonical polyadic finite basis representation (CP-FBR).

In the present work, we introduce a simple means of obtaining an analytical (i.e., grid-free) canonical polyadic (CP) representation of a multidimensional function that is expressed in terms of a set of discrete data. For this, we make use of an initial CP guess, even not fully converged, and a set of auxiliary basis functions [finite basis representation (FBR)]. The resulting CP-FBR expression constitutes the CP counterpart of our previous Tucker sum-of-products-FBR approach. However, as is well-known, CP expressions are much more compact. This has obvious advantages in high-dimensional quantum dynamics. The power of CP-FBR lies in the fact that it requires a grid much coarser than the one needed for the dynamics. In a subsequent step, the basis functions can be interpolated to any desired density of grid points. This is useful, for instance, when different initial conditions (e.g., energy content) of a system are to be considered. We show the application of the method to bound systems of increased dimensionality: H2 (3D), HONO (6D), and CH4 (9D).

Time-Resolved Hanbury Brown–Twiss Interferometry of On-Chip Biphoton Frequency Combs Using Vernier Phase Modulation

Biphoton frequency combs (BFCs) are promising quantum sources for large-scale and high-dimensional quantum information and networking systems. In this context, the spectral purity of individual frequency bins will be critical for realizing quantum networking protocols like teleportation and entanglement swapping. Measurement of the temporal autocorrelation function of the unheralded signal or idler photons comprising the BFC is a key tool for characterizing their spectral purity and in turn verifying the utility of the biphoton state for networking protocols. Yet the experimentally obtainable precision for measuring BFC correlation functions is often severely limited by detector jitter. The fine temporal features in the correlation function---not only of practical value in quantum information, but also of fundamental interest in the study of quantum optics---are lost as a result. We propose a scheme to circumvent this challenge through electro-optic phase modulation, experimentally demonstrating time-resolved Hanbury Brown--Twiss characterization of BFCs generated from an integrated 40.5-GHz ${\mathrm{Si}}_{3}{\mathrm{N}}_{4}$ microring, up to a $3\ifmmode\times\else\texttimes\fi{}3$-dimensional two-qutrit Hilbert space. Through slight detuning of the electro-optic drive frequency from the comb's free spectral range, our approach leverages Vernier principles to magnify temporal features, which would otherwise be averaged out by detector jitter. We demonstrate our approach under both continuous-wave and pulsed-pumping regimes, finding excellent agreement with theory. Our method reveals not only the collective statistics of the contributing frequency bins but also their temporal shapes---features lost in standard fully integrated autocorrelation measurements.

Construction of efficient Schmidt-number witnesses for high-dimensional quantum states

Recent progress in quantum optics has led to setups that are able to prepare high-dimensional quantum states for quantum information processing tasks. As such, it is of importance to benchmark the states generated by these setups in terms of their quantum mechanical properties, such as their Schmidt numbers, i.e., the number of entangled degrees of freedom. In this paper, we develop an iterative algorithm that finds Schmidt number witnesses tailored to the measurements available in specific experimental setups. We then apply the algorithm to find a witness that requires the measurement of a number of density matrix elements that scales linearly with the local dimension of the system. As a concrete example, we apply our construction method to an implementation with photonic temporal modes.

Coloured vortex beams with incoherent white light illumination.

The orbital angular momentum is a fundamental degree of freedom of light wavefronts, currently exploited in applications where information capacity is a key requirement, such as optical communication, super-resolution imaging and high-dimensional quantum computing. However, generating orbital angular momentum beams requires spatio-temporally coherent light sources (lasers or supercontinuum sources), because incoherent light would smear out the doughnut features of orbital angular momentum beams, forming polychromatic or obscured orbital angular momentum beams instead. Here we show generation of coloured orbital angular momentum beams using incoherent white light. Spatio-temporal coherence is achieved by miniaturizing spiral phase plates and integrating them with structural colour filters, three-dimensionally printed at the nanoscale. Our scheme can in principle generate multiple helical eigenstates and combine colour information into orbital angular momentum beams independently. These three-dimensional optical elements encoded with colour and orbital angular momentum information substantially increase the number of combinations for optical anti-counterfeiting and photonic lock-key devices in a pairwise fashion.

High-Dimensional Entanglement-Enabled Holography.

As an important imaging technique, holography has been realized with different physical dimensions of light, including polarization, wavelength, and time. Recently, quantum holography has been demonstrated by utilizing polarization entangled state with the advantages of high robustness and enhanced spatial resolution, comparing with classical holography. However, the polarization is only a two-dimensional degree of freedom, which greatly limits the capacity of quantum holography. Here, we propose a method to realize high-dimensional quantum holography by using high-dimensional orbital angular momentum (OAM) entanglement. A high-capacity OAM-encoded quantum holographic system can be obtained by multiplexing a wide range of OAM-dependent holographic images. Proof-of-principle experiments with four- and six-dimensional OAM entangled states have been implemented and verify the feasibility of our idea. Our experimental results also demonstrate that the high-dimensional quantum holography shows a high robustness to classical noise. What is more, the level of security of the holographic imaging encryption system can be greatly improved in our high-dimensional quantum holography.

Editorial: Laser field manipulation and its advanced applications

Laser field manipulation is currently one of hot topics in the field of photonics. A wide variety of novel beams, for instance, vectorial vortex beams [1], orbital angular momentum (OAM) comb [2], toroidal vortices [3], high-dimensional beam arrays [4], can be well generated through tailoring various spatial and temporal degrees of freedom (DoFs) as OAM, spin angular momentum (SAM), phase, time/frequency, amplitude, and wave vector. Such novel beams from laser field manipulation have inspired lots of advanced applications covering classical and quantum physics as large-capacity optical communications, lidar, optical tweezer, laser processing, high-dimensional quantum entanglement, and also gravity wave detection [5]. In recent years, many efforts have been paid on laser field manipulation and achieve a leaping development. Hence, to show recent advances in laser field manipulation and their enabled applications, we organize this research topic, and expect to motivate more state-of-art scenarios.The seven published papers in this topic involve both fundamental and engineering research, regarding complex laser field tailoring and applications. M. Zhang et al. In summary, this research topic collects seven representative work of state-of-art laser field manipulation and its advanced applications. We expect this topic will build a bridge of distinct sub-areas integration, and further promote the development of laser field manipulation.

A perspective on the manipulation of orbital angular momentum states in nonlinear optics

Orbital angular momentum (OAM) of light has been widely investigated in optical manipulation, optical communications, optical storage, and precision measurement. In recent years, the studies of OAM are expanded to nonlinear and quantum optics, paving a way to high-quality nonlinear imaging, high-capacity quantum communication, and many other promising applications. In this Perspective, we first summarize the fundamental research on OAM in nonlinear optics. Then, we introduce its recent applications in nonlinear imaging (including nonlinear spiral imaging and OAM-multiplexing nonlinear holography) and high-dimensional quantum entanglement. In particular, we highlight the manipulations of OAM through various functional nonlinear photonic crystals. Finally, we discuss the further developments of OAM-based nonlinear and quantum techniques in the near future.

High-dimensional quantum key distribution implemented with biphotons

We present a high-dimensional measurement device-independent (MDI) quantum key distribution (QKD) protocol employing biphotons to encode information. We exploit the biphotons as qutrits to improve the tolerance to error rate. Qutrits have a larger quantum system; hence they carry more bits of classical information and have improved robustness against eavesdropping compared to qubits. Notably, our proposed protocol is independent of measurement devices, thus eliminating the possibility of side-channel attacks. Also, we employ the finite key analysis approach to study the performance of our proposed protocol under realistic conditions where finite resources are used. Furthermore, we simulated the secret key rate for the proposed protocol in terms of the transmission distance for different fixed amounts of signals. The results prove that this protocol achieves a considerable secret key rate for a moderate transmission distance of 90 km by using 10^{16} signals. Moreover, the expected secret key rate was simulated to examine our protocol’s performance at various intrinsic error rate values, Q=(0.3%,0.6%,1%) caused by misalignment and instability due to the optical system. These results show that reasonable key rates are achieved with a minimum data size of about 10^{14} signals which are realizable with the current technology. Thus, implementing MDI-QKD using finite resources while allowing intrinsic errors due to the optical system makes a giant step forward toward realizing practical QKD implementations.

Long distance entanglement and high-dimensional quantum teleportation in the Fermi–Hubbard model

The long distance entanglement in finite size open Fermi–Hubbard chains, together with the end-to-end quantum teleportation are investigated. We show the peculiarity of the ground state of the Fermi–Hubbard model to support maximum long distance entanglement, which allows it to operate as a quantum resource for high fidelity long distance quantum teleportation. We determine the physical properties and conditions for creating scalable long distance entanglement and analyze its stability under the effect of the Coulomb interaction and the hopping amplitude. Furthermore, we show that the choice of the measurement basis in the protocol can drastically affect the fidelity of quantum teleportation and we argue that perfect information transfer can be attained by choosing an adequate basis reflecting the salient properties of the quantum channel, i.e. Hubbard projective measurements.

Manipulation of continuous variable orbital angular momentum squeezing and entanglement by pump shaping.

Spatially structured quantum states, such as orbital angular momentum (OAM) squeezing and entanglement, is currently a popular topic in quantum optics. The method of generating and manipulating spatial quantum states on demand needs to be explored. In this paper, we generated OAM mode squeezed states of -5.4 dB for the L G0+1 mode and -5.3 dB for the L G0-1 mode directly by an optical parametric oscillator (OPO) for the first time. Additionally, we demonstrated that the OAM mode squeezed and entangled states were respectively generated by manipulating the nonlinear process of the OPO by controlling the relative phase of two beams of different modes, thus making two different spatial multimode pump beams. We characterized the Laguerre-Gaussian (LG) entangled states by indirectly measuring the squeezing for the H G 10(45∘) mode and H G 10(135∘) mode, and directly measuring the entanglement between the L G0+1 and L G0-1 modes. The effective manipulation of the OAM quantum state provides a novel insight into the continuous variable quantum state generation and construction on demand for high-dimensional quantum information and quantum metrology.

Learning Quantum Distributions with Variational Diffusion Models

It is challenging to identify the state of many-body quantum systems, as recovering density matrices underlying the quantum state typically requires computational resources scale exponentially to the system size. In this work, we introduce the variational diffusion model (VDM) to efficiently learn high-dimensional quantum distributions with high fidelity, which is essential to realize the fast reconstruction of quantum states. We build up the VDM suitable for dealing with the high-dimensional quantum samples, and then perform numerical experiments to test our model and other autoregressive models, including recurrent neural network and transformer. It is found that the VDM can achieve a modest better performance with fewest parameters than other two to learn the distribution as desired. Our results pave the way to applying diffusion models to solve hard problems in the quantum domain.

Nonlinear topological pumping in momentum space lattice of ultracold atoms

Topological pumping enables the quantized transport of matter waves through an adiabatic evolution of the system, which plays an essential role in the applications of transferring quantum states and exploring the topological properties in higher-dimensional quantum systems. Recently, exploring the interplay between novel topological pumping and interactions has attracted growing attention in topological systems, such as nonlinear topological pumping induced by interactions. So far, the experimental realizations of the nonlinear topological pumps have been realized only in the optical waveguide systems with Kerr nonlinearity. It is still necessary to further explore the phenomenon in different systems. Here, we present an experimental proposal for realizing the nonlinear topological pumping via a one-dimensional (1D) off-diagonal Aubry-André-Harper (AAH) model with mean-field interactions in the momentum space lattice of ultracold atoms. In particular, we develop a numerical method for calculating the energy band of the nonlinear systems. With numerical calculations, we first solve the nonlinear energy band structure and soliton solution of the 1D nonlinear off-diagonal AAH model in the region of weak interaction strengths. The result shows that the lowest or the highest energy band is modulated in the nonlinear system of <inline-formula><tex-math id="M2">\begin{document}$ g > 0$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230740_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230740_M2.png"/></alternatives></inline-formula> or <inline-formula><tex-math id="M3">\begin{document}$ g < 0$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230740_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230740_M3.png"/></alternatives></inline-formula>, respectively. The eigenstates of the associated energy bands have the features of the soliton solutions. We then show that the topological pumping of solitons exhibits quantized transport characteristics. Moreover, we numerically calculate the Chern number associated with the lowest and highest energy bands at different interaction strengths. The result shows that the quantized transport of solitons is determined by the Chern number of the associated energy band of the system from which solitons emanate. Finally, we propose a nonlinear topological pumping scheme based on a momentum lattice experimental system with <inline-formula><tex-math id="M4">\begin{document}$ ^{7}\text{Li}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230740_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230740_M4.png"/></alternatives></inline-formula> atoms. We can prepare the initial state, which is approximately the distribution of the soliton state of the lowest energy band, and calculate the dynamical evolution of this initial state in the case of <inline-formula><tex-math id="M5">\begin{document}$ U > 0$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230740_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230740_M5.png"/></alternatives></inline-formula>. Also, we analyze the influence of adiabatic evolution conditions on the pumping process, demonstrating the feasibility of nonlinear topological pumping in the momentum lattice system. Our study provides a feasible route for investigating nonlinear topological pumping in ultracold atom systems, which is helpful for further exploring the topological transport in nonlinear systems, such as topological phase transitions and edge effects induced by nonlinearity.

Symmetry resolved entanglement of excited states in quantum field theory. Part I. Free theories, twist fields and qubits

The excess entanglement resulting from exciting a finite number of quasiparticles above the ground state of a free integrable quantum field theory has been investigated quite extensively in the literature. It has been found that it takes a very simple form, depending only on the number of excitations and their statistics. There is now mounting evidence that such formulae also apply to interacting and even higher-dimensional quantum theories. In this paper we study the entanglement content of such zero-density excited states focusing on the symmetry resolved entanglement, that is on 1+1D quantum field theories that possess an internal symmetry. The ratio of charged moments between the excited and grounds states, from which the symmetry resolved entanglement entropy can be obtained, takes a very simple and universal form, which in addition to the number and statistics of the excitations, now depends also on the symmetry charge. Using form factor techniques, we obtain both the ratio of moments and the symmetry resolved entanglement entropies in complex free theories which possess U(1) symmetry. The same formulae are found for simple qubit states.