High-dimensional Quantum Research Articles

Multichannel Quantum Emission with On-Chip Emitter-Coupled Holographic Metasurfaces.

Multichannel quantum emission is in high demand for advanced quantum photonic applications such as quantum communications, quantum computing, and quantum cryptography. However, to date, the most common way for shaping photon emission from quantum emitters (QEs) is to utilize free-standing (external) bulky optical components. Here, we develop the multichannel holography approach for flexibly designing on-chip QE-coupled metasurfaces that make use of nonradiatively QE-excited surface plasmon polaritons for generating far-field quantum emission, which propagates in designed directions carrying specific spin and orbital angular momenta (SAM and OAM, respectively). We further design, fabricate, and characterize on-chip quantum light sources of multichannel quantum emission encoded with different SAMs and OAMs. The holography-based inverse design approach developed and demonstrated on-chip quantum light sources with multiple degrees of freedoms, thereby enabling a powerful platform for quantum nanophotonics, especially relevant for advanced quantum photonic applications, e.g., high-dimensional quantum information processing.

High Dimensional Quantum Digital Signature Depending on Entanglement Swapping

While a single qubit information can be carried with a single photon in 2−dimensional quantum technology, it is possible to carry more than one qubit information with a single photon in high-dimensional quantum technologies. The amount of qubit to be transported depends on the size of the system obtained in the high dimension. In other words, the more high-dimensional quantum structure it creates, the more qubit-carrying system is obtained. In this study, a high dimensional quantum digital signature(QDS) scheme is proposed for multi-partied by using entanglement swapping and super-dense coding. QDS, which is proposed as highdimensional, allows more data and high-rate keys to be transferred. Security analysis of propesed QDS in high-dimensional show that the propablity of anyone obtaining information is much lower than in qubit states. Since all data(quantum and classic) in this protocol is instantly sent by using entanglement channels it is more resilient eavesdropping attacks. Today, developments in highdimensional experimental studies show that the high-dimensional QDS proposed in this study can be implemented practically.

High-dimensional time-frequency entanglement in a singly-filtered biphoton frequency comb

High-dimensional quantum entanglement is a cornerstone for advanced technology enabling large-scale noise-tolerant quantum systems, fault-tolerant quantum computing, and distributed quantum networks. The recently developed biphoton frequency comb (BFC) provides a powerful platform for high-dimensional quantum information processing in its spectral and temporal quantum modes. Here we propose and generate a singly-filtered high-dimensional BFC via spontaneous parametric down-conversion by spectrally shaping only the signal photons with a Fabry-Pérot cavity. High-dimensional energy-time entanglement is verified through Franson-interference recurrences and temporal correlation with low-jitter detectors. Frequency- and temporal- entanglement of our singly-filtered BFC is then quantified by Schmidt mode decomposition. Subsequently, we distribute the high-dimensional singly-filtered BFC state over a 10 km fiber link with a post-distribution time-bin dimension lower bounded to be at least 168. Our demonstrations of high-dimensional entanglement and entanglement distribution show the singly-filtered quantum frequency comb’s capability for high-efficiency quantum information processing and high-capacity quantum networks.

Compact all-fiber quantum-inspired LiDAR with over 100 dB noise rejection and single photon sensitivity

Entanglement and correlation of quantum light can enhance LiDAR sensitivity in the presence of strong background noise. However, the power of such quantum sources is fundamentally limited to a stream of single photons and cannot compete with the detection range of high-power classical LiDAR transmitters. To circumvent this, we develop and demonstrate a quantum-inspired LiDAR prototype based on coherent measurement of classical time-frequency correlation. This system uses a high-power classical source and maintains the high noise rejection advantage of quantum LiDARs. In particular, we show that it can achieve over 100dB rejection (with 100ms integration time) of indistinguishable (with statistically identical properties in every degree of freedom) in-band noise while still being sensitive to single photon signals. In addition to the LiDAR demonstration, we also discuss the potential of the proposed LiDAR receiver for quantum information applications. In particular, we propose the chaotic quantum frequency conversion technique for coherent manipulation of high dimensional quantum states of light. It is shown that this technique can provide improved performance in terms of selectivity and efficiency as compared to pulse-based quantum frequency conversion.

A hybrid-qudit representation of digital RGB images

Quantum image processing is an emerging topic in the field of quantum information and technology. In this paper, we propose a new quantum image representation of RGB images with deterministic image retrieval, which is an improvement over all the similar existing representations in terms of using minimum resource. We use two entangled quantum registers constituting of total 7 qutrits to encode the color channels and their intensities. Additionally, we generalize the existing encoding methods by using both qubits and qutrits to encode the pixel positions of a rectangular image. This hybrid-qudit approach aligns well with the current progress of NISQ devices in incorporating higher dimensional quantum systems than qubits. We then describe the image encoding method using higher-order qubit-qutrit gates, and demonstrate the decomposition of these gates in terms of simpler elementary gates. We use the Google Cirq’s quantum simulator to verify the image preparation in both the ideal noise-free scenario and in presence of realistic noise modelling. We show that the complexity of the image encoding process is linear in the number of pixels. Lastly, we discuss the image compression and some basic RGB image processing protocols using our representation.

Interferometric imaging of amplitude and phase of spatial biphoton states

High-dimensional biphoton states are promising resources for quantum applications, ranging from high-dimensional quantum communications to quantum imaging. A pivotal task is fully characterizing these states, which is generally time-consuming and not scalable when projective measurement approaches are adopted; however, new advances in coincidence imaging technologies allow for overcoming these limitations by parallelizing multiple measurements. Here we introduce biphoton digital holography, in analogy to off-axis digital holography, where coincidence imaging of the superposition of an unknown state with a reference state is used to perform quantum state tomography. We apply this approach to single photons emitted by spontaneous parametric down-conversion in a nonlinear crystal when the pump photons possess various quantum states. The proposed reconstruction technique allows for a more efficient (three orders of magnitude faster) and reliable (an average fidelity of 87%) characterization of states in arbitrary spatial modes bases, compared with previously performed experiments. Multiphoton digital holography may pave the route toward efficient and accurate computational ghost imaging and high-dimensional quantum information processing.

Data re-uploading with a single qudit

Quantum two-level systems, i.e., qubits, form the basis for most quantum machine learning approaches that have been proposed throughout the years. However, higher dimensional quantum systems constitute a promising alternative and are increasingly explored in theory and practice. Here, we explore the capabilities of multi-level quantum systems, so-called qudits, for their use in a quantum machine learning context. We formulate classification and regression problems with the data re-uploading approach and demonstrate that a quantum circuit operating on a single qudit is able to successfully learn highly non-linear decision boundaries of classification problems such as the MNIST digit recognition problem. We demonstrate that the performance strongly depends on the relation between the qudit states representing the labels and the structure of labels in the training data set. Such a bias can lead to substantial performance improvement over qubit-based circuits in cases where the labels, the qudit states, and the operators employed to encode the data are well-aligned. Furthermore, we elucidate the influence of the choice of the elementary operators and show that a squeezing operator is necessary to achieve good performances. We also show that there exists a trade-off for qudit systems between the number of circuit-generating operators in each processing layer and the total number of layers needed to achieve a given accuracy. Finally, we compare classification results from numerically exact simulations and their equivalent implementation on actual IBM quantum hardware. The findings of our work support the notion that qudit-based algorithms exhibit attractive traits and constitute a promising route to increasing the computational capabilities of quantum machine learning approaches.

On-chip generation of single-photon circularly polarized single-mode vortex beams.

Generation of single photons carrying spin and orbital angular momenta (SAM and OAM) opens enticing perspectives for exploiting multiple degrees of freedom for high-dimensional quantum systems. However, on-chip generation of single photons encoded with single-mode SAM-OAM states has been a major challenge. Here, by using carefully designed anisotropic nanodimers fabricated atop a substrate, supporting surface plasmon polariton (SPP) propagation, and accurately positioned around a quantum emitter (QE), we enable nonradiative QE-SPP coupling and the SPP outcoupling into free-space propagating radiation featuring the designed SAM and OAM. We demonstrate on-chip room-temperature generation of well-collimated (divergence < 7.5°) circularly polarized (chirality > 0.97) single-mode vortex beams with different topological charges (𝓁 = 0, 1, and 2) and high single-photon purity, g(2)(0) < 0.15. The developed approach can straightforwardly be extended to produce multiple, differently polarized, single-mode single-photon radiation channels and enable thereby realization of high-dimensional quantum sources for advanced quantum photonic technologies.

High Dimensional Quantum Machine Learning With Small Quantum Computers

Quantum computers hold great promise to enhance machine learning, but their current qubit counts restrict the realisation of this promise. To deal with this limitation the community has produced a set of techniques for evaluating large quantum circuits on smaller quantum devices. These techniques work by evaluating many smaller circuits on the smaller machine, that are then combined in a polynomial to replicate the output of the larger machine. This scheme requires more circuit evaluations than are practical for general circuits. However, we investigate the possibility that for certain applications many of these subcircuits are superfluous, and that a much smaller sum is sufficient to estimate the full circuit. We construct a machine learning model that may be capable of approximating the outputs of the larger circuit with much fewer circuit evaluations. We successfully apply our model to the task of digit recognition, using simulated quantum computers much smaller than the data dimension. The model is also applied to the task of approximating a random 10 qubit PQC with simulated access to a 5 qubit computer, even with only relatively modest number of circuits our model provides an accurate approximation of the 10 qubit PQCs output, superior to a neural network attempt. The developed method might be useful for implementing quantum models on larger data throughout the NISQ era.

Arbitrarily structured quantum emission with a multifunctional metalens

Structuring light emission from single-photon emitters (SPEs) in multiple degrees of freedom is of great importance for quantum information processing towards higher dimensions. However, traditional control of emission from quantum light sources relies on the use of multiple bulky optical elements or nanostructured resonators with limited functionalities, constraining the potential of multi-dimensional tailoring. Here we introduce the use of an ultrathin polarisation-beam-splitting metalens for the arbitrary structuring of quantum emission at room temperature. Owing to the complete and independent polarisation and phase control at the single meta-atom level, the designed metalens enables simultaneous mapping of quantum emission from ultra-bright defects in hexagonal boron nitride and imprinting of an arbitrary wavefront onto orthogonal polarisation states of the sources. The hybrid quantum metalens enables simultaneous manipulation of multiple degrees of freedom of a quantum light source, including directionality, polarisation, and orbital angular momentum. This could unleash the full potential of solid-state SPEs for their use as high-dimensional quantum sources for advanced quantum photonic applications.

Proposal for the complete high-dimensional Greenberger–Horne–Zeilinger state measurement

Abstract A theoretical proposal for the complete analysis of high-dimensional Greenberger–Horne–Zeilinger (GHZ) state is presented in this Letter. We first demonstrate the approach for the complete three-photon GHZ state measurement in three dimensions, and then generalize it to the situation of N-photon system in d dimensions. In our approach, the photonic hyperentanglement and quantum Fourier transform are both utilized. The presented proposal will be useful for the high-dimensional multi-photon quantum computation and quantum communication.

Complete Hierarchy for High-Dimensional Steering Certification.

High-dimensional quantum steering can be seen as a test for the dimensionality of entanglement, where the devices at one side are not characterized. As such, it is an important component in quantum informational protocols that make use of high-dimensional entanglement. Although it has been recently observed experimentally, the phenomenon of high-dimensional steering is lacking a general certification procedure. We provide necessary and sufficient conditions to certify the entanglement dimension in a steering scenario. These conditions are stated in terms of a hierarchy of semidefinite programs, which can also be used to quantify the phenomenon using the steering dimension robustness. To demonstrate the practical viability of our method, we characterize the dimensionality of entanglement in steering scenarios prepared with maximally entangled states measured in mutually unbiased bases. Our methods give significantly stronger bounds on the noise robustness necessary to experimentally certify high-dimensional entanglement.

Digital twin of the atmospheric turbulence channel based on self-supervised deep learning algorithm

High dimensional quantum entanglement based on orbital angular momentum (OAM) can provide infinite freedom theoretically, providing a significant improvement on the capacity of the quantum communication. However, the vortex beam that carries OAM signal can be easily distorted by atmospheric turbulence and can degrade the performance of the system. Consequently, for the operation, administration and maintenance of quantum system, an accurate digital twin model of the turbulent channel is necessary. Digital twin model is a mathematical model which can reflect the influence of atmospheric channel on quantum system by theoretical analysis. Nevertheless, it is challenging to achieve for the complex mechanism of atmospheric turbulence. To address this problem, deep learning (DL) techniques have been studied recently. Whereas, for the training of DL, a massive number of labeled samples are needed, i.e., the actual free-space channel, which are hard to be obtained in practical systems. The pool generalization also hinders the use of these DL-based algorithms in practice. To overcome the above challenges, we propose a self-supervised DL algorithm, which does not need any labeled samples in advance, meaning the training of the algorithm can be restarted any time once the environment changes. Compared with previous studies, the proposed algorithm can better suite as the digital twin of the turbulent channel. To verify the performance of the proposed algorithm, we perform extensive verification, whose results demonstrate the superior performance of the proposed method.

Compact implementation of high-dimensional mutually partially unbiased bases protocol

Transverse spatial mode of light is crucial in high-dimensional quantum key distribution (QKD). However, applications in realistic scenarios suffer from mode-dependent loss and the complexity of system, making it impractical to achieve higher-dimensional, longer-distance and low-cost communications. A mutually partially unbiased bases (MPUBs) protocol has been proposed to fundamentally eliminate the effects induced by mode-dependent loss for long propagation distances and limited sizes of apertures. Here, we demonstrate the first implementation of the MPUBs protocol in dimensions of and 6. By performing a controlled unitary transformation, we can actively switch the measurement basis and enable a compact measurement system. In consequence, a higher encoding dimension is available under finite system resources, resulting in higher key rates and stronger noise resistance. Our work enhances the practicability of MPUBs protocol, and may promote the applications of high-dimensional QKD in quantum networks.

Spacetime-emergent ring toward tabletop quantum gravity experiments

We propose a way to discover, in tabletop experiments, spacetime-emergent materials, that is, materials holographically dual to higher-dimensional quantum gravity systems under the AdS/CFT. The emergence of the holographic spacetime is verified by a mathematical imaging transform of the response function on the material. We consider theories on a one-dimensional ring-shaped material and compute the response to a scalar source locally put at a point on the ring. When the theory on the material has a gravity dual, the imaging in the low-temperature phase exhibits a distinct difference from the ordinary materials: The spacetime-emergent material can look into the holographically emergent higher-dimensional curved spacetime and provides an image as if a wave had propagated there. Therefore the image is an experimental signature of the spacetime emergence. We also estimate the temperature, ring size, and source frequency usable in experiments, with an example of a quantum critical material, ${\mathrm{TlCuCl}}_{3}$.

Experimental Test of High-Dimensional Quantum Contextuality Based on Contextuality Concentration.

Contextuality is a distinctive feature of quantum theory and a fundamental resource for quantum computation. However, existing examples of contextuality in high-dimensional systems lack the necessary robustness required in experiments. Here, we address this problem by identifying a family of noncontextuality inequalities whose maximum quantum violation grows with the dimension of the system. At first glance, this contextuality is the single-system version of multipartite Bell nonlocality taken to an extreme form. What is interesting is that the single-system version achieves the same degree of contextuality but uses a Hilbert space of lower dimension. That is, contextuality "concentrates" as the degree of contextuality per dimension increases. We show the practicality of this result by presenting an experimental test of contextuality in a seven-dimensional system. By simulating sequences of quantum ideal measurements with destructive measurements and repreparation in an all-optical setup, we report a violation of 68.7 standard deviations of the simplest case of the noncontextuality inequalities identified. Our results advance the investigation of high-dimensional contextuality, its connection to the Clifford algebra, and its role in quantum computation.

Convex Optimization for Nonequilibrium Steady States on a Hybrid Quantum Processor.

Finding the transient and steady state properties of open quantum systems is a central problem in various fields of quantum technologies. Here, we present a quantum-assisted algorithm to determine the steady states of open system dynamics. By reformulating the problem of finding the fixed point of Lindblad dynamics as a feasibility semidefinite program, we bypass several well-known issues with variational quantum approaches to solving for steady states. We demonstrate that our hybrid approach allows us to estimate the steady states of higher dimensional open quantum systems and discuss how our method can find multiple steady states for systems with symmetries.

Diffractive Theory Study of Twisted Light’s Evolution during Phase-Only OAM Manipulations

Twisted light, or orbital angular momentum (OAM) carrying beams or photons, is a pillar of structured photonics, a booming subfield of modern optics. The generation and transformation of twisted light, which lie with coupling topological charges into target light’s wavefunctions, are usually performed by phase-only OAM manipulations. The practical twisted lights, however, obtained by this method are actually noneigen modes of free space, leading to an evolution through the diffractive propagation. Here, we present a general theoretical frame for accurately describing this evolution. Based on the theory, the whole diffractive propagation history in a typical OAM-manipulation loop, converting Gaussian light into a twisted one and then reconverting back, is demonstrated via a set of exact analytical solutions. These results provide a powerful tool for analyzing the transverse profiles of twisted light through the diffractive evolution, as a guideline for studying the science of structured light, which would provide guidelines for research studies in nonlinear optics and high-dimensional quantum information technology based on OAM-degree of freedom.

Exploring disordered quantum spin models with a multilayer multiconfigurational approach

Numerical simulations of quantum spin models are crucial for a profound understanding of many-body phenomena in a variety of research areas in physics. An outstanding problem is the availability of methods to tackle systems that violate area-laws of entanglement entropy. Such scenarios cover a wide range of compelling physical situations including disordered quantum spin systems among others. In this work, we employ a numerical technique referred to as multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) to evaluate the ground state of several disordered spin models. ML-MCTDH has previously been used to study problems of high-dimensional quantum dynamics in molecular and ultracold physics but is here applied to study spin systems for the first time. We exploit the inherent flexibility of the method to present results in one and two spatial dimensions and treat challenging setups that incorporate long-range interactions as well as disorder. Our results suggest that the hierarchical multi-layering inherent to ML-MCTDH allows to tackle a wide range of quantum many-body problems such as spin dynamics of varying dimensionality.

High-dimensional quantum information processing on programmable integrated photonic chips

High-dimensional quantum information processing on programmable integrated photonic chips