High-dimensional Quantum States Research Articles

Quantum Universally Composable Oblivious Linear Evaluation

Oblivious linear evaluation is a generalization of oblivious transfer, whereby two distrustful parties obliviously compute a linear function, f(x)=ax+b, i.e., each one provides their inputs that remain unknown to the other, in order to compute the output f(x) that only one of them receives. From both a structural and a security point of view, oblivious linear evaluation is fundamental for arithmetic-based secure multi-party computation protocols. In the classical case, oblivious linear evaluation protocols can be generated using oblivious transfer, and their quantum counterparts can, in principle, be constructed as straightforward extensions using quantum oblivious transfer. Here, we present the first, to the best of our knowledge, quantum protocol for oblivious linear evaluation that, furthermore, does not rely on quantum oblivious transfer. We start by presenting a semi-honest protocol, and then extend it to the dishonest setting employing a commit−and−open strategy. Our protocol uses high-dimensional quantum states to obliviously compute f(x) on Galois Fields of prime and prime-power dimension. These constructions utilize the existence of a complete set of mutually unbiased bases in prime-power dimension Hilbert spaces and their linear behaviour upon the Heisenberg-Weyl operators. We also generalize our protocol to achieve vector oblivious linear evaluation, where several instances of oblivious linear evaluation are generated, thus making the protocol more efficient. We prove the protocols to have static security in the framework of quantum universal composability.

Multi-party semi-quantum private comparison protocol of size relation based on two-dimensional Bell states

Abstract Currently, all quantum private comparison protocols based on two-dimensional quantum states can only compare equality. It is only through the use of high-dimensional quantum states that it is possible to compare the size relation in existing work. In addition, it is difficult to manipulate the high-dimensional quantum states under the existing conditions of quantum information processing, leading to low practicality and engineering feasibility of protocols for comparing size relation. Considering this situation, an innovative protocol is proposed in this paper. The proposed protocol can make size comparison by exploiting more manageable two-dimensional Bell states, which significantly enhances its feasibility with current quantum technologies. Simultaneously, the proposed protocol enables multiple participants to compare their privacies with the semi-quantum model. The communication process of the protocol is simulated on the IBM Quantum Experience platform to verify its effectiveness. Security analysis shows that the proposed protocol can withstand common attacks while preserving the privacies of all participants. Thus, the devised protocol may provide an important reference for the implementation of quantum private size comparison protocols.

Higher-Dimensional Communications Using Multimode Fibers and Compact Components to Enable a Dense Set of Communicating Channels

Higher-dimensional communications are of interest for multiple reasons, including increasing the classical transmission capacity and, more recently, the quantum state transfer through fibers using the many modes within the fiber. For quantum communications, this enables an increase in the number of bits per photon, increasing quantum fidelity, increasing error thresholds and enabling hyperentanglement transfer, among other possibilities. A high-dimensional quantum state transfer can be transported through multimode fiber using the many modes available. However, this transfer of information through multimode optical fiber is limited by attenuation and mode coupling among the various spatial and polarization modes. Here, we consider how this mode coupling impacts the transfer process. We consider the fiber’s modal properties, including orbital angular momentum, modal group numbers, and principal modes. We also investigate and propose input and output optical components, as well as fiber properties, which better mitigate the deleterious effects of mode coupling. We use the WKB approximation to the scaler wave equation as a guidance to quantify this coupling and then implement corrections to this approximation using exact solutions to the scaler wave equation. We consider methods to circumvent this mode coupling using optical fiber designs, holographic optical components and devices that are commercially available today. Some of these components, such as the holographic gratings and lenses, could be implemented using flat optics.

Families of Schmidt-number witnesses for high dimensional quantum states

Higher dimensional entangled states demonstrate significant advantages in quantum information processing tasks. The Schmidt number is a quantity of the entanglement dimension of a bipartite state. Here we build families of k-positive maps from the symmetric information complete positive operator-valued measurements and mutually unbiased bases, and we also present the Schmidt number witnesses, correspondingly. At last, based on the witnesses obtained from mutually unbiased bases, we show the distance between a bipartite state and the set of states with a Schmidt number less than k.

Quantifying quantum entanglement via machine learning models

Quantifying entanglement measures for quantum states with unknown density matrices is a challenging task. Machine learning offers a new perspective to address this problem. By training machine learning models using experimentally measurable data, we can predict the target entanglement measures. In this study, we compare various machine learning models and find that the linear regression and stack models perform better than others. We investigate the model’s impact on quantum states across different dimensions and find that higher-dimensional quantum states yield better results. Additionally, we investigate which measurable data has better predictive power for target entanglement measures. Using correlation analysis and principal component analysis, we demonstrate that quantum moments exhibit a stronger correlation with coherent information among these data features.

Entanglement criterion and strengthened Bell inequalities based on the Pearson correlation

Entanglement is a property associated with quantum correlations and represents a key resource in several applications of quantum technology. Therefore, the ability to characterize entanglement is important at both foundational and practical levels. This work demonstrates how the Pearson correlation coefficient can be used to establish an entanglement criterion for quantum systems of two qubits. This criterion is then used to prove that a proposed conjecture is correct for the case of two qubits, which allows to efficiently identify entanglement without the need of complete prior knowledge of the quantum state. For higher dimensional quantum states the conjecture is demonstrated to be false through counter-examples, therefore a modified version of it is proposed. Finally, two new strengthened Bell inequalities are derived, which are also efficient in entanglement identification.

NOON-state interference in the frequency domain

The examination of entanglement across various degrees of freedom has been pivotal in augmenting our understanding of fundamental physics, extending to high dimensional quantum states, and promising the scalability of quantum technologies. In this paper, we demonstrate the photon number path entanglement in the frequency domain by implementing a frequency beam splitter that converts the single-photon frequency to another with 50% probability using Bragg scattering four-wave mixing. The two-photon NOON state in a single-mode fiber is generated in the frequency domain, manifesting the two-photon interference with two-fold enhanced resolution compared to that of single-photon interference, showing the outstanding stability of the interferometer. This successful translation of quantum states in the frequency domain will pave the way toward the discovery of fascinating quantum phenomena and scalable quantum information processing.

Multipartite high-dimensional quantum state engineering via discrete-time quantum walk

Multipartite high-dimensional quantum state engineering via discrete-time quantum walk

Application of quantum machine learning in a Higgs physics study at the CEPC

Machine learning has blossomed in recent decades and has become essential in many fields. It significantly solved some problems in particle physics — particle reconstruction, event classification, etc. However, it is now time to break the limitation of conventional machine learning with quantum computing. A support-vector machine algorithm with a quantum kernel estimator (QSVM-Kernel) leverages high-dimensional quantum state space to identify a signal from backgrounds. In this study, we have pioneered employing this quantum machine learning algorithm to study the [Formula: see text] process at the Circular Electron–Positron Collider (CEPC), a proposed Higgs factory to study electroweak symmetry breaking of particle physics. Using 6 qubits on quantum computer simulators, we optimized the QSVM-Kernel algorithm and obtained a classification performance similar to the classical support-vector machine algorithm. Furthermore, we have validated the QSVM-Kernel algorithm using 6-qubits on quantum computer hardware from both IBM and Origin Quantum: the classification performances of both are approaching noiseless quantum computer simulators. In addition, the Origin Quantum hardware results are similar to the IBM Quantum hardware within the uncertainties in our study. Our study shows that state-of-the-art quantum computing technologies could be utilized by particle physics, a branch of fundamental science that relies on big experimental data.

Research progress of integrated quantum light sources with orbital angular momentum

Quantum light sources are one of key devices for quantum information processing, and they are also the important foundation for applications such as in quantum computing, quantum communication, and quantum simulation. Improving the capacity of quantum information coding by using the quantum light source is a major challenge in the development of quantum information technology. Photons with a helical phase front can carry a discrete, unlimited but quantized amount of orbital angular momentum (OAM). The infinite number of states with different OAMs can greatly increase the capacity of optical communication and information processing in quantum regimes. To date photons carrying OAM have mainly been generated by using bulk crystals, which limits the efficiency and the scalability of the source. With the advancement of quantum photonic technology, many significant quantum photonic devices can now be realized on integrated chips. However, creating high-dimensional OAM quantum states at a micro-nano scale is still a challenge. And the research of harnessing high-dimensional OAM mode by using integrated quantum photonic technologies is still in its infancy. Here, the authors review the recent progress and discuss the integrated quantum light sources with OAM. The authors introduce the research progress of using OAM for both single photons and entangled photons and emphasize the exciting work on pushing boundaries in high-dimensional quantum states. This may pave the way for the research and practical applications of high-dimensional quantum light sources.

High-dimensional Encoding in the Round-Robin Differential-Phase-Shift Protocol

In quantum key distribution (QKD), protocols are tailored to adopt desirable experimental attributes, including high key rates, operation in high noise levels, and practical security considerations. The round-robin differential phase shift protocol (RRDPS), falling in the family of differential phase shift protocols, was introduced to remove restrictions on the security analysis, such as the requirement to monitor signal disturbances, improving its practicality in implementations. While the RRDPS protocol requires the encoding of single photons in high-dimensional quantum states, at most, only one bit of secret key is distributed per sifted photon. However, another family of protocols, namely high-dimensional (HD) QKD, enlarges the encoding alphabet, allowing single photons to carry more than one bit of secret key each. The high-dimensional BB84 protocol exemplifies the potential benefits of such an encoding scheme, such as larger key rates and higher noise tolerance. Here, we devise an approach to extend the RRDPS QKD to an arbitrarily large encoding alphabet and explore the security consequences. We demonstrate our new framework with a proof-of-concept experiment and show that it can adapt to various experimental conditions by optimizing the protocol parameters. Our approach offers insight into bridging the gap between seemingly incompatible quantum communication schemes by leveraging the unique approaches to information encoding of both HD and DPS QKD.

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.

Generation of high-dimensional qudit quantum states via two-dimensional quantum walks

Generation of high-dimensional qudit quantum states via two-dimensional quantum walks

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.

Quantum structured light in high dimensions

Structured light has become topical of late, where controlling light in all its degrees of freedom has offered novel states of light long predicted, enhanced functionality in applications, and a modern toolbox for probing fundamental science. Structuring light as single photons and entangled states allows the spatial modes of light to be used to encode a large alphabet, accessing high dimensional Hilbert spaces for fundamental tests of quantum mechanics and improved quantum information processing tasks. In this tutorial, we outline the basic concepts of high dimensional quantum states expressed in a basis of spatial modes (structured light) and explain how to create, control, and detect such quantum states in the laboratory with a focus on transverse spatial modes such as the orbital angular momentum and pixel (position) modes. Finally, we highlight some example applications of such quantum structured light, from communications to imaging.

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.

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.

An Examination of Quantum Information Processing Through Quantum Cryptography; A study

"Along with these developments, personal microwave technology has enabled strong non-linear effects at the photon level, leading to readily observable novel parameter regimes in quantum optics. Circuit QED has opened up new opportunities to explore the rich physics of quantum information processing (QIP) and quantum optics (QO), making them scalable on the road to quantum computing. However, we must also discuss some of the challenges involved. Quantum Technologies (QT) is a cross-disciplinary field that has made great progress in recent years. Technologies that can explicitly represent individual quantum states, as well as superposition and entanglement, are now being developed to exploit the 'strange' properties of quantum mechanics. In quantum communication, individual or entangled photons are used to securely send data, while quantum simulation utilizes well-controlled quantum systems that are less accessible. Interest is growing in higher dimensional quantum states and quantum communication, as the extended availability of Hilbert space and greater information capacity, along with increased noise elasticity, offer many advantages and new research possibilities. Let's focus our attention on the benefits of higher dimensional quantum states for quantum communication, as shown by Kuditz and others. Nevertheless, it has been demonstrated that higher dimensional quantum states can also provide improvements in many other areas."

Quantum Bell nonlocality cannot be shared under a special kind of bilateral measurements for high-dimensional quantum states

Quantum Bell nonlocality is an important quantum phenomenon. Recently, the shareability of Bell nonlocality under unilateral measurements has been widely studied. In this study, we consider the shareability of quantum Bell nonlocality under bilateral measurements. Under a specific class of projection operators, we find that quantum Bell nonlocality cannot be shared for a limited number of times, as in the case of unilateral measurements. Our proof is analytical, and our measurement strategies can be generalized to higher-dimensional cases.

High-dimensional multi-input quantum random access codes and mutually unbiased bases

Quantum random access codes (QRACs) provide a basic tool for demonstrating the advantages of quantum resources and protocols, which have a wide range of applications in quantum information processing tasks. However, the investigation and application of high-dimensional $(d)$ multi-input $(n)$ $n^{(d)}\rightarrow1$ QRACs are still lacking. Here, we present a general method to find the maximum success probability of $n^{(d)}\rightarrow1$ QRACs. In particular, we give the analytical solution for maximum success probability of $3^{(d)}\rightarrow1$ QRACs when measurement bases are mutually unbiased bases (MUBs). Based on the analytical solution, we show the relationship between MUBs and $n^{(d)}\rightarrow1$ QRACs. First, we provide a systematic method of searching for the operational inequivalence of MUBs (OI-MUBs) when the dimension $d$ is a prime power. Second, we theoretically prove that, surprisingly, the commonly used Galois MUBs are not the optimal measurement bases to obtain the maximum success probability of $n^{(d)}\rightarrow1$ QRACs, which indicates a breakthrough according to the traditional conjecture regarding the optimal measurement bases. Furthermore, based on high-fidelity high-dimensional quantum states of orbital angular momentum, we experimentally achieve two-input and three-input QRACs up to dimension 11. We experimentally confirm the OI-MUBs when $d=5$. Our results open alternative avenues for investigating the foundational properties of quantum mechanics and quantum network coding.