Maurice R. Kibler
Spin bases of relevance for quantum systems with cyclic symmetry as well as for quantum information and quantum computation are constructed from the theory of angular momentum. This approach is connected to the use of generalized Pauli matrices (in dimension d) arising from a polar decomposition of the group SU(2). Numerous examples are given for d=2, 3 and 4.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We analytically derive a decoherence model for orbital angular momentum states of a photon in a multimode optical fiber and show that rate of decoherence scales exponentially with $l^2$, where $l$ is the azimuthal mode order.~We also show numerically that for large values of $l$ the orbital angular momentum photon state completely dephases.~However for lower values of $l$ the decoherence can be minimized by using dynamical decoupling to allow for qudit high-bandwidth quantum communication and similar applications. \end{abstract}
We propose a method for generation of entangled photonic states in high dimensions, the so-called qudits, by exploiting quantum correlations of Orbital Angular Momentum (OAM) entangled photons, produced via Spontaneous Parametric Down Conversion. Diffraction masks containing $N$ angular slits placed in the path of twin photons define a qudit space of dimension $N^2$, spanned by the alternative pathways of OAM-entangled photons. We quantify the high-dimensional entanglement of path-entangled photons by the Concurrence, using an analytic expression valid for pure states. We report numerical resu…
Ptychographic estimation of qudit states encoded in the angular position and orbital angular momentum of single photons
本文提出将叠层衍射量子类比方法应用于单光子角位置与轨道角动量编码的高维量子态估计，通过二进制空间滤波器和OAM模式后选择实现，模拟验证有效并讨论实验可行性。
The application of high-dimensional quantum systems (qudits) in quantum computing and communications seems to be a promising avenue due to the possibility of increasing the amount of information encoded in one physical carrier. In this work, we propose a method for implementing single-qudit gates for qudits based on light modes with orbital angular momentum. Method for logical qudits encoding, which ensures the quasi-cyclicity of operations, is introduced. Based on the protocol for converting the orbital angular momentum of light in the Raman quantum memory scheme [Vashukevich E.A. et. al. PRA…
Using angular position-orbital angular momentum entangled photons, we propose an experiment to generate maximally entangled states of $D$-dimensional quantum systems, the so called qudits, by exploiting correlations of parametric down-converted photons. Angular diffraction masks containing $N$-slits in the arms of each twin photon define a qudit space of dimension $N^2$, spanned by the alternative pathways of the photons. Due to phase-matching conditions, the twin photons will pass only by symmetrically opposite angular slits, generating maximally entangled states between these different paths…
Demonstration of subspace-search variational quantum eigensolver using photonic orbital angular momentum qudits
研究针对NISQ硬件VQE多局限于基态的问题，利用光子轨道角动量qudits实现SSVQE，估算HeH⁺分子和海森堡链的激发态能量，确立光子qudits是高效的激发态量子模拟途径。
Entangled quantum states play an important role in quantum information science and also in quantum mechanics fundamental investigations. Implementation and characterization of techniques allowing for easy preparation of entangled states are important steps in such fields. Here we generated entangled quantum states encoded in photons transversal paths, obtained by pumping a non-linear crystal with multiple transversal Gaussian beams. Such approach allows us to generate entangled states of two qubits and two qutrits encoded in Gaussian transversal path of twin photons. We make a theoretical anal…
Quantum state tomography (QST) is an essential tool for characterizing an unknown quantum state. Recently, QST has been performed for entangled qudits based on orbital angular momentum, time-energy uncertainty, and frequency bins. Here, we propose a QST for time-bin qudits, with which the number of measurement settings scales linearly with dimension $d$. Using the proposed scheme, we performed QST for a four-dimensional time-bin maximally entangled state with 16 measurement settings. We successfully reconstructed the density matrix of the entangled qudits, with which the average fidelity of th…
A new version of quantum hashing technique is developed wherein a quantum hash is constructed as a sequence of single-photon high-dimensional states (qudits). A proof-of-principle implementation of the high-dimensional quantum hashing protocol using orbital-angular momentum encoding of single photons is implemented. It is shown that the number of qudits decreases with increase of their dimension for an optimal ratio between collision probability and decoding probability of the hash. Thus, increasing dimension of information carriers makes quantum hashing with single photons more efficient.
We prepare qudits based on angular multimode biphoton states by modulating the pump angular spectrum. The modes are prepared in the Schmidt basis and their intensity distributions do not overlap in space. This allows one to get rid of filtering losses while addressing single modes and to realize a single-shot qudit readout.
The codification in higher dimensional Hilbert Spaces (whose logical basis states are dubbed qudits in analogy with bidimensional qubits) presents various advantages both for Quantum Information applications and for studies on Foundations of Quantum Mechanics. Purpose of this review is to introduce qudits, to summarize their application to Quantum Communication and researches on Local Realism and, finally, to describe some recent experiment for realizing them. A Little more in details: after a short introduction, we will consider the advantages of testing local realism with qudits, discussing …
Implementation and representation of qudit multi-controlled unitaries and hypergraph states by N-body angular momentum couplings
研究通过N体角动量耦合实现量子位多控制酉算子及超图态的表示，在三量子位特殊情况阐述要点，将三量子位三方控制酉算子按二体角动量耦合分解，给出光学系统实现示例并定义新的角动量超图态。
Experimental demonstration of optimal measurement for unambiguously discriminating asymmetric qudit states
本研究通过光子轨道角动量态实验实现了对不对称四态的最优测量，为高维量子信息处理提供了新的方法。
One of the main challenges in quantum technologies is the ability to control individual quantum systems. This task becomes increasingly difficult as the dimension of the system grows. Here we propose a general setup for cyclic permutations $X_d$ in $d$ dimensions, a major primitive for constructing arbitrary qudit gates. Using orbital angular momentum states as a qudit, the simplest implementation of the $X_d$ gate in $d$ dimensions requires a single quantum sorter $S_d$ and two spiral phase plates. We then extend this construction to a generalised $X_d(p)$ gate to perform a cyclic permutation…
The capability to generate and manipulate quantum states in high-dimensional Hilbert spaces is a crucial step for the development of quantum technologies, from quantum communication to quantum computation. One-dimensional quantum walk dynamics represents a valid tool in the task of engineering arbitrary quantum states. Here we affirm such potential in a linear-optics platform that realizes discrete-time quantum walks in the orbital angular momentum degree of freedom of photons. Different classes of relevant qudit states in a six-dimensional space are prepared and measured, confirming the feasi…
Quantum Teleportation, the transfer of the state of one quantum system to another without direct interaction between both systems, is an important way to transmit information encoded in quantum states and to generate quantum correlations (entanglement) between remote quantum systems. So far, for photons, only superpositions of two distinguishable states (one ``qubit'') could be teleported. Here we show how to teleport a ``qudit'', i.e. a superposition of an arbitrary number $d$ of distinguishable states present in the orbital angular momentum of a single photon using $d$ beam splitters and $d$…
Spectral-angular parametrization of open qudit dynamics: gap coordinates, Cartan structure, and GKLS decoupling
本文提出了一种在有限维希尔伯特空间中描述混合态密度矩阵的参数化方法，适用于开放量子系统的时间演化。通过将密度矩阵分解为谱参数和角变量，结合李代数解释，为量子系统动力学提供了新的分析框架。
Bloch sphere analog of qudits using Heisenberg-Weyl Operators
本研究基于Heisenberg-Weyl算符基提出多能级量子系统布洛赫矢量参数化方法，以三能级qutrit为例分析其非实心布洛赫球结构，并将方法推广到qudit，可用于量子基、量子映射及系综评估等研究。
Orbital angular momentum based intra- and inter- particle entangled states generated via a quantum dot source
本文利用量子点源生成具有轨道角动量的单光子态，通过内联和外联纠缠实验实现高维量子态制备。
The spatial modes of photons are one realization of a QuDit, a quantum system that is described in a D-dimensional Hilbert space. In order to perform quantum information tasks with QuDits, a general class of D-dimensional unitary transformations is needed. Among these, cyclic transformations are an important special case required in many high-dimensional quantum communication protocols. In this paper, we experimentally demonstrate a cyclic transformation in the high-dimensional space of photonic orbital angular momentum (OAM). Using simple linear optical components, we show a successful four-f…
Synthetic high angular momentum spin dynamics in a microwave oscillator
本文提出一种在微波振荡器中按需修改谐振子以实现谐振qudit通用控制的新协议，通过线性和非线性操作合成高角动量自旋动力学，验证了SU(2)旋转和逻辑门集，为超导电路模拟高角动量量子磁性开辟了新途径。
Building an efficient quantum memory in high-dimensional Hilbert spaces is one of the fundamental requirements for establishing high-dimensional quantum repeaters, where it offers many advantages over two-dimensional quantum systems, such as a larger information capacity and enhanced noise resilience. To date, there have been no reports about how to achieve an efficient high-dimensional quantum memory. Here, we experimentally realize a quantum memory that is operational in Hilbert spaces of up to 25 dimensions with a storage efficiency of close to 60%. The proposed approach exploits the spatia…
To maximize average information gain for a classical measurement, all outcomes of an observation must be equally likely. The condition of equally likely outcomes may be enforced in quantum theory by ensuring that one's state $ρ$ is maximally different, or complementary, to the measured observable. This requires the ability to perform unitary operations on the state, conditioned on the results of prior measurements. We consider the case of measurement of a component of angular momentum for a qudit (a $D$-dimensional system, with $D=2J+1$). For weak or continuous-in-time (i.e. repeated weak) mea…
We develop a distillation protocol for multilevel qubits (qudits) using generalized beam splitters like in the proposal of Pan et al. for ordinary qubits. We find an acceleration with respect to the scheme of Bennet et al. when extended to qudits. It is also possible to distill entangled pairs of photons carrying orbital angular momenta (OAM) states that conserves the total angular momenta as those produced in recent experiments.
A simple argument is presented that explicitly shows how to construct an arbitrary quantum gate acting on orbital angular momentum (OAM) of single photons. The scheme can be applied to implement subspace multiplexing, where a single high-dimensional OAM qudit represents effectively a stack of multiple independent lower-dimensional qudits. A special subclass of unitaries composed of single-photon controlled gates is studied in detail and notable examples of the general approach are discussed. The generalization of the simple argument leads to the parallelization scheme, which results in the sav…
The generation and control of quantum correlations in high-dimensional systems is a major challenge in the present landscape of quantum technologies. Achieving such non-classical high-dimensional resources will potentially unlock enhanced capabilities for quantum cryptography, communication and computation. We propose a protocol that is able to attain entangled states of $d$-dimensional systems through a quantum-walk-based {\it transfer \& accumulate} mechanism involving coin and walker degrees of freedom. The choice of investigating quantum walks is motivated by their generality and versatili…
We analyze Weyl algebra of quantum angular momentum system and construct qubit subalgebra out of it. We show that the commutant of this qubit subalgebra is isomorphic to the original algebra and prove the tensor product structure between qubit subalgebra and its commutant. This construction can be iterated to construct arbitrary number of qubit subalgebras from a single quantum system. We show a simple experimental realization of this proposed scheme using orbital angular momentum of single photons. We briefly discuss about construction of qudit subalgbra and generalization to other infinite d…
Tracking the Evolution of Near-Field Photonic Qubits into High-Dimensional Qudits via State Tomography
研究通过量子态层析成像揭示光子在近场与自由空间间耦合时量子信息的演化，发现近场TAM量子比特转化为自由空间纠缠于SAM和OAM的四态，验证了高维量子电路芯片开发的新方法。
Teleportation plays an important role in the communication of quantum information between the nodes of a quantum network and is viewed as an essential ingredient for long-distance Quantum Cryptography. We describe a method to teleport the quantum information carried by a photon in a superposition of a number $d$ of light modes (a "qudit") by the help of $d$ additional photons based on transcription. A qudit encoded into a single excitation of $d$ light modes (in our case Laguerre-Gauss modes which carry orbital angular momentum) is transcribed to $d$ single-rail photonic qubits, which are spat…
Geometric properties of qudit systems
本文利用最大熵原理和广义 Bloch 向量及特殊酉群不变量研究 qudit 系统热态的几何性质，并通过 J=1、J=3/2 及 Lipkin-Meshkov-Glick 模型展示量子相变和相图。
The ability to completely characterize the state of a quantum system is an essential element for the emerging quantum technologies. Here, we present a compressed-sensing inspired method to ascertain any rank-deficient qudit state, which we experimentally encode in photonic orbital angular momentum. We efficiently reconstruct these qudit states from a few scans with an intensified CCD camera. Since it requires only a few intensity measurements, our technique would provide an easy and accurate way to identify quantum sources, channels, and systems.
We present a scalable set of universal gates and multiply controlled gates in a qudit basis through a bijective mapping from N qubits to qudits with D = 2^N levels via rotations in U(2). For each of the universal gates (H, CNOT, and T), as well as the NOT gate and multiply-controlled-Z gates, we describe a systematic approach to identifying the set of U(2) rotations required to implement each gate for any qudit of size N and with minimal use of an ancilla level. The qudit gates are analyzed in terms of the total rotation count and gate depth as the system scales with D. We apply the qudit-basi…
Measurement-device-independent (MDI) method is a way to solve all detector side-channel attacks in quantum key distribution (QKD). However, very little work has been done on experimentally feasible qudit-based MDI-QKD scheme although the famous (qudit-based) round-robin differential-phase-shift (RRDPS) scheme is vulnerable to attacks on uncharacterized detectors. Here we report a mother-of-all QKD protocol on which all provably secure qubit-based QKD schemes known to date including the RRDPS and the so-called Chau15 schemes are based. We also report an experimentally feasible MDI system via op…
Heralded qudit-based high-dimensional entanglement generation for hybrid photon-emitter system by waveguide-mediated scattering
本文提出一种基于波导介导散射的预示式方案，通过输入端口选择在混合光子-发射体系统中生成4维及更高维的多量子dit最大纠缠，无需辅助量子dit且具有鲁棒保真度，可推广至一般d维n量子dit纠缠态。
The orbital angular momentum of light (OAM) provides a promising approach for the implementation of multidimensional states (qudits) for quantum information purposes. In order to characterize the degradation undergone by the information content of qubits encoded in a bidimensional subspace of the orbital angular momentum degree of freedom of photons, we study how the state fidelity is affected by a transverse obstruction placed along the propagation direction of the light beam. Emphasis is placed on the effects of planar and radial hard-edged aperture functions on the state fidelity of Laguerr…
Measurement-based quantum computing with qudit stabilizer states
该研究提出利用替代四维资源态进行基于测量的量子计算，通过优化内在门结构提升计算效率。
Low depth measurement-based quantum computation with qudits ($d$-level systems) is investigated and a precise relationship between this powerful model and qudit quantum circuits is derived in terms of computational depth and size complexity. To facilitate this investigation a qudit `unbounded fan-out' circuit model, in which a qudit may be quantum-copied into an arbitrary number of ancillas in a single time-step, is introduced and shown to be capable of implementing interesting $n$-qudit unitaries in constant depth. A procedure for reducing the quantum computational depth in the measurement-ba…
High-dimensional degrees of freedom of photons can encode more quantum information than their two-dimensional counterparts. While the increased information capacity has advantages in quantum applications (such as quantum communication), controlling and manipulating these systems has been challenging. Here we show a method to perform lossless arbitrary high-dimensional Pauli-X gates for single photon. The X-gate consists of a cyclic permutation of qudit basis vectors, and, together with the Z gate, forms the basis for performing arbitrary transformations. We propose an implementation of such ga…
Scalable platform for qudit-based quantum computing using polar molecules
本文提出利用极性分子的旋转态构建可扩展的量子处理器，通过光学镊子阵列实现指数级态空间扩展，无需增加量子比特维度，实现通用量子门集。
Qudit Dynamical Decoupling on a Superconducting Quantum Processor
本文针对多能级量子位系统易退相干的问题，基于海森堡-魏尔群提出动态解耦协议，在超导处理器上实验验证了其能有效抑制退相干和交叉克尔耦合，显著提升贝尔态保真度，为可扩展量子计算铺路。
In comparison to qubit-based protocols, qudit-based quantum key distribution (QKD) ones gen- erally allow two cooperative parties to share unconditionally secure keys under a higher channel noise. However, it is very hard to prepare and measure the required quantum states in qudit-based protocols in general. One exception is the recently proposed highly error tolerant qudit-based proto- col known as the Chau15 [1]. Remarkably, the state preparation and measurement in this protocol can be done relatively easily since the required states are phase encoded almost like the diagonal basis states of…
Qudit-ADAPT-VQE: an adaptive variational algorithm with counterdiabatic-inspired improvements for qudits
本研究提出量子位版ADAPT-VQE算法，引入受逆绝热驱动启发的算子池，在求解最大3割问题时精度更高、原生门成本更低，且能应对优化空间局部陷阱，为量子位变分量子算法提供可扩展框架。
Heralded High-Dimensional Photon-Photon Quantum Gate
本文提出了一种实现高维光子-光子量子门的协议，通过四维qudit-qudit CPF门实验验证，展示了高维光子信息处理的进展。
We observe that lattice surgery, a model of fault-tolerant qubit computation, generalises straightforwardly to arbitrary finite-dimensional qudits. The generalised model is based on the group algebras $\mathbb{C}\mathbb{Z}_d$ for $d \geq 2$. It still requires magic state injection for universal quantum computation. We relate the model to the ZX-calculus, a diagrammatic language based on Hopf-Frobenius algebras.
Near-term Application Engineering Challenges in Emerging Superconducting Qudit Processors
本文回顾了基于超导transmon与射频腔的qudit量子处理器在NISQ时代的应用前景，并分析了其在模拟、组合优化和量子机器学习中的工程机遇与挑战。
In quantum computation and information science, the geometrical representations based on the Bloch sphere representation for transformations of two state systems have been traditionally used. While this representation is very useful for the two state qubit, it cannot be generalized easily to multiple states like that of qudits and when it is generalized, it looses its simple geometrical representation. This paper proposes the use of an alternative representation in quantum information and computation for qubits as well as qudits based on the Majorana representation on the Riemann Sphere, which…
Recent research in generalizing quantum computation from 2-valued qudits to d-valued qudits has shown practical advantages for scaling up a quantum computer. A further generalization leads to quantum computing with hybrid qudits where two or more qudits have different finite dimensions. Advantages of hybrid and d-valued gates (circuits) and their physical realizations have been studied in detail by Muthukrishnan and Stroud (Physical Review A, 052309, 2000), Daboul et al. (J. Phys. A: Math. Gen. 36 2525-2536, 2003), and Bartlett et al (Physical Review A, Vol.65, 052316, 2002). In both cases, a …
Quantum tomography makes it possible to obtain comprehensive information about certain logical elements of a quantum computer. In this regard, it is a promising tool for debugging quantum computers. The practical application of tomography, however, is still limited by systematic measurement errors. Their main source are errors in the quantum state preparation and measurement procedures. In this work, we investigate the possibility of suppressing these errors in the case of ion-based qudits. First, we will show that one can construct a quantum measurement protocol that contains no more than a s…
Qudit is a multi-level computational unit alternative to the conventional 2-level qubit. Compared to qubit, qudit provides a larger state space to store and process information, and thus can provide reduction of the circuit complexity, simplification of the experimental setup and enhancement of the algorithm efficiency. This review provides an overview of qudit-based quantum computing covering a variety of topics ranging from circuit building, algorithm design, to experimental methods. We first discuss the qudit gate universality and a variety of qudit gates including the pi/8 gate, the SWAP g…
Fault-Tolerant Encoding of Logical Qudits in Spin Systems
本文提出了一种在有限维自旋系统中实现容错逻辑四维子空间的通用框架，展示了距离为3、5的编码及通用2t+1距离码，具有更小的希尔伯特空间维度和多项式缩放的逻辑操作与纠错协议。
Universal quantum computing with qubits embedded in trapped-ion qudits
本文提出在囚禁离子量子比特（维度 d=3 至 8）中嵌入量子比特的量子电路编译方法，利用单量子比特操作和 Molmer-Sorensen 门实现单、双及多量子比特门，为扩展量子处理器提供新途径。
Resource states that contain nontrivial symmetry-protected topological order are identified for universal single-qudit measurement-based quantum computation. Our resource states fall into two classes: one as the qudit generalizations of the 1D qubit cluster state, and the other as the higher-symmetry generalizations of the spin-1 Affleck-Kennedy-Lieb-Tasaki (AKLT) state, namely, with unitary, orthogonal, or symplectic symmetry. The symmetry in cluster states protects information propagation (identity gate), while the higher symmetry in AKLT-type states enables nontrivial gate computation. This…
In measurement-based quantum computing (MBQC), computation is carried out by a sequence of measurements and corrections on an entangled state. Flow, and related concepts, are powerful techniques for characterising the dependence of the corrections on previous measurement outcomes. We introduce flow-based methods for MBQC with qudit graph states, which we call Zd-flow, when the local dimension is an odd prime. Our main results are proofs that Zd-flow is a necessary and sufficient condition for a strong form of outcome determinism. Along the way, we find a suitable generalisation of the concept …
We propose a new method for implementing mutually unbiased generation and measurement of time-bin qudits using a cascade of electro-optic phase modulator -- coded fiber Bragg grating pairs. Our approach requires only a single spatial mode and can switch rapidly between basis choices. We obtain explicit solutions for dimensions $d=2,3,4$ that realize all $d+1$ possible mutually unbiased bases and analyze the performance of our approach in quantum key distribution. Given its practicality and compatibility with current technology, our approach provides a promising springboard for scalable process…
We investigate the interplay between mutual unbiasedness and product bases for multiple qudits of possibly different dimensions. A product state of such a system is shown to be mutually unbiased to a product basis only if each of its factors is mutually unbiased to all the states which occur in the corresponding factors of the product basis. This result implies both a tight limit on the number of mutually unbiased product bases which the system can support and a complete classification of mutually unbiased product bases for multiple qubits or qutrits. In addition, only maximally entangled stat…
An Error-aware and Adaptive Method for the Estimation of Quantum Observables on Qudit-Based Quantum Computers
本文提出AQUIRE方法，通过构建贝叶斯模型准确估计量子比特量子计算机上可观测量的均值和误差，并通过数值模拟和离子阱量子处理器实验验证其有效性。
Proof-of-concept Quantum Simulator based on Molecular Spin Qudits
本研究展示了首个基于分子自旋量子点(qudits)系综和射频宽带光谱仪的原型量子模拟器，通过模拟磁化强度的量子隧穿和横向场伊辛模型证明了其可操作性，为分子自旋量子点在量子技术中的实际应用迈出了重要一步。
Realizing quantum gates with optically-addressable $^{171}$Yb$^{+}$ ion qudits
本研究利用线性阱中光寻址的$^{171}$Yb$^{+}$离子qudit构建量子处理器寄存器，基于435.5 nm四极时钟跃迁的Zeeman子能级进行编码，并实现了包含单qudit旋转和双qudit Molmer-Sorensen操作的通用门集。
Blind quantum computing with different qudit resource state architectures
本文探讨了多级量子系统在无监督量子计算中的应用，通过多级量子资源态实现安全的云量子计算，比较了不同资源态架构的开销及隐藏策略。
We consider the problem of time-optimal realization of the quantum Fourier transform gate for a single qudit with number of levels d from 3 to 8. As a qudit the quadrupole nucleus with spin I > 1/2 controlled by NMR is considered. We calculate the dependencies of the gate error on the duration of radio-frequency pulse obtained by numerical optimization using Krotov-based algorithm. It is shown that the dependences of minimum time of QFT gate implementation on qudit dimension are different for integer and half-integer spins.
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。