Direct High-Dimensional Quantum Communication with Tunable Bases via Sequential Non-Demolition Measurements

Mutually unbiased bases (MUBs) play a key role in many protocols in quantum science, such as quantum key distribution. However, defining MUBs for arbitrary high-dimensional systems is theoretically difficult, and measurements in such bases can be hard to implement. We show experimentally that efficient quantum state reconstruction of a high-dimensional multipartite quantum system can be performed by considering only the MUBs of the individual parts. The state spaces of the individual subsystems are always smaller than the state space of the composite system. Thus, the benefit of this method is that MUBs need to be defined for the small Hilbert spaces of the subsystems rather than for the large space of the overall system. This becomes especially relevant where the definition or measurement of MUBs for the overall system is challenging. We illustrate this approach by implementing measurements for a high-dimensional system consisting of two photons entangled in the orbital angular momentum degree of freedom, and we reconstruct the state of this system for dimensions of the individual photons from d = 2 to 5.

Quantum entanglement is essential for the realization of distributed computing and has been implemented in various types of two-level systems. However, high-dimensional quantum protocols are rarely investigated both theoretically and experimentally, despite the remarkable advantages that high-dimensional quantum systems exhibit over two-level systems for certain quantum information and computing tasks. Here, we propose asymmetric protocols that utilize different dimensional systems to prepare the stator and achieve remote state operations with the assistance of shared N-partite graph states. Our protocols demonstrate convincing control power and security, with all implementations achievable through local operations and classical communications. The experimental realization of high-dimensional quantum systems and operations is presented using current technology. Our work contributes towards achieving arbitrary high-dimensional quantum protocols and paves the way for implementing high-dimensional quantum communication and computation.

Quantum information science has leaped forward with the exploration of high-dimensional quantum systems, offering greater potential than traditional qubits in quantum communication and quantum computing. To advance the field of high-dimensional quantum technology, a significant effort is underway to progressively enhance the entanglement dimension between two particles. An alternative effective strategy involves not only increasing the dimensionality but also expanding the number of particles that are entangled. We present an experimental study demonstrating multi-partite quantum non-locality beyond qubit constraints, thus moving into the realm of strongly entangled high-dimensional multi-particle quantum systems. In the experiment, quantum states were encoded in the path degree of freedom (DoF) and controlled via polarization, enabling efficient operations in a two-dimensional plane to prepare three- and four-particle Greenberger-Horne-Zeilinger (GHZ) states in three-level systems. Our experimental results reveal ways in which high-dimensional systems can surpass qubits in terms of violating local-hidden-variable theories. Our realization of multiple complex and high-quality entanglement technologies is an important primary step for more complex quantum computing and communication protocols.

We investigate correlations among complementary observables. In particular,\nwe show how to take advantage of mutually unbiased bases (MUBs) for the\nefficient detection of entanglement in arbitrarily high-dimensional,\nmultipartite and continuous variable quantum systems. The introduced\nentanglement criteria are relatively easy to implement experimentally since\nthey require only a few local measurement settings. In addition, we establish a\nlink between the separability problem and the maximum number of mutually\nunbiased bases -- opening a new avenue in this long-standing open problem.\n

High-dimensional quantum systems have been used to reveal interesting fundamental physics and to improve information capacity and noise resilience in quantum information processing. However, it remains a significant challenge to realize universal two-photon quantum gates in high dimensions with high success probability. Here, by considering an ion-cavity QED system, we theoretically propose, to the best of our knowledge, the first high-dimensional, deterministic, and universal two-photon quantum gate. By using an optical cavity embedded with a single trapped Ca+40 ion, we achieve a high average fidelity larger than 98% for a quantum controlled phase-flip gate in four-dimensional space, spanned by photonic spin angular momenta and orbital angular momenta. Our proposed system can be an essential building block for high-dimensional quantum information processing, and also provides a platform for studying high-dimensional cavity QED. Published by the American Physical Society 2024

High-dimensional quantum system provides a higher capacity of quantum channel, which exhibits potential applications in quantum information processing. However, high-dimensional universal quantum logic gates is difficult to achieve directly with only high-dimensional interaction between two quantum systems and requires a large number of two-dimensional gates to build even a small high-dimensional quantum circuits. In this paper, we propose a scheme to implement a general controlled-flip (CF) gate where the high-dimensional single photon serve as the target qudit and stationary qubits work as the control logic qudit, by employing a three-level Λ-type system coupled with a whispering-gallery-mode microresonator. In our scheme, the required number of interaction times between the photon and solid state system reduce greatly compared with the traditional method which decomposes the high-dimensional Hilbert space into 2-dimensional quantum space, and it is on a shorter temporal scale for the experimental realization. Moreover, we discuss the performance and feasibility of our hybrid CF gate, concluding that it can be easily extended to a 2n-dimensional case and it is feasible with current technology.

A deterministic qudit-dependent high-dimensional photonic quantum gate with weak cross-kerr nonlinearity

Quantum information science has extensive applications in various research fields, such as information, physics and computer science. It is well known that the quantum properties of a system exhibit many unique advantages in the security of information transmission and processing, computation, and the improvement of channel capacity. Quantum information includes several research fields, for example, quantum communication, quantum computing and so on. In the past 30 years, the development of quantum communication, quantum computing and quantum information processing has made great progress in both theory and experiments. As a fundamental resource for quantum information processing, entanglement is a key element for many applications, such as quantum key distribution, quantum teleportation, quantum dense coding, quantum secure direct communication and quantum metrology. Because of the weak interaction with the environment and the degrees of freedom, entangled photons are the excellent candidates as the quantum-information carrier. Several remarkable experiments have been performed with the photonic entanglement. However, it is necessary to share a pair of entangled photons between the communicating parties in advance in these quantum information processes. Furthermore, the application of hyperentanglement, the entanglement of photon pairs simultaneously existing in more than one degree of freedom, has been widely studied for the reason that it can improve the channel capacity of quantum communications and implement hyperparallel computing, such as the quantum error-correcting code, quantum repeater and deterministic entanglement purification. Moreover, the quantum logic gates play an essential role in quantum information processing which attracts much attention on the designing of the quantum logic gates. Depending on the coherent dynamics of the cavity quantum electrodynamical system, deterministic quantum gate operations between the quantum systems can be realized. Here in this review, by considering high-dimensional quantum systems, several high-dimensional quantum protocols are presented. They can greatly improve the capacity of quantum channel and noise immunity, which exhibits potential applications in quantum information processing. This review describes the development of quantum computing and quantum information processing using hyperentanglement. And the entangled photons in single degree of freedom and multi-degrees of freedom are used to illustrate the two-dimensional and high-dimensional quantum information processing schemes. Finally, the latest progress and further applications of quantum computing and quantum information processing are introduced.

This paper proposed a novel dynamic quantum secret sharing protocol in high-dimensional quantum system. Via transmitting the particles circularly and local unitary operations, the dealer and all agents can share the multi-particle entangled GHZ state in high-dimensional quantum system. The proposed protocol allows a dealer to share the predetermined dits without directly distributing any piece of shares to agents. To recover the secrets, dealer and all agents only need to perform the single-particle measurement operation and then implement the simple modular arithmetic operation according to their corresponding measurement results. Besides, in the proposed protocol, only a little fraction of entangled GHZ states are employed for eavesdropping check instead of lots of decoy (or detecting) particles used in previous protocols. Since the protocol is designed in the high-dimensional quantum system, it makes our protocol have higher resource capacity and better security in detecting the illegal eavesdropper than former protocols designed in two-dimensional quantum system. Security analyses indicate that the proposed protocol is immune to general attacks of intercept-and-resend, entangle-and-measure, collusion, and revoked a dishonest agent. Furthermore, the efficiency of proposed DQSS protocol in noise environment is deduced through quantum fidelity. The obtained results indicate that the efficiency of proposed protocol decreases with the increase in channel noise parameter and it has a quite different efficiency in four types of noise, i.e., dit-flip, d-phase-flip, amplitude-damping and depolarizing.

Quantum communication (QC) represents a key enabler for many quantum applications. However, low information rates and short propagation distances, limit the development of this field and its practical applications. High-dimensional (Hi-D) QC can address these challenges enhancing the information rate and the systems error tolerance. We report our recent results on Hi-D quantum communication where we prove the capability of preparing, manipulating, transmitting and measuring Hi-D quantum states through multi-core and multimode fiber.

Quantum information theory and the second quantum revolution have brought us within grasping distance of quantum computers, the building block of which is the qubit. Like their classical counter parts---the bit---they are two-dimensional, reaching their power when embedded in an network of many interacting qubits. However, many quantum systems are not two-dimensional in nature, but high dimensional. In this thesis, I explore---both experimentally and theoretically---several applications of encoding and processing information in high dimensional quantum systems. I consider information encoded in the spatial, temporal, and phase space distributions of optical systems. I further analyse the evolution of these systems using the theory of closed and open quantum systems, conditional dynamics and Fock state master equations. These results highlight the unique advantages of high dimensional quantum systems in the sub-disciplines quantum foundations, quantum simulation and quantum sensing. Our results clearly demonstrate that high dimensional quantum information presents many unique applications that could be fostered into new technology.

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.

Growing interest has been invested in exploring high-dimensional quantum systems, for their promising perspectives in certain quantum tasks. How to characterize a high-dimensional entanglement structure is one of the basic questions to take full advantage of it. However, it is not easy for us to catch the key feature of high-dimensional entanglement, for the correlations derived from high-dimensional entangled states can be possibly simulated with copies of lower-dimensional systems. Here, we follow the work of Kraft et al. [Phys. Rev. Lett. 120, 060502 (2018)], and present the experimental realizing of creation and detection, by the normalized witness operation, of the notion of genuine high-dimensional entanglement, which cannot be decomposed into lower-dimensional Hilbert space and thus form the entanglement structures existing in high-dimensional systems only. Our experiment leads to further exploration of high-dimensional quantum systems.

We present a feasible proposal for quantum tomography of qubit and qutrit states via mutually unbiased measurements in dispersively coupled driven cavity QED systems. We first show that measurements in the mutually unbiased bases (MUBs) are practically implemented by projecting the detected states onto the computational basis after performing appropriate unitary transformations. The measurement outcomes can then be determined by detecting the steady-state transmission spectra (SSTS) of the driven cavity. It is found that all the measurement outcomes for each MUB (i.e., all the diagonal elements of the density matrix of each detected state) can be read out directly from only one kind of SSTS. In this way, we numerically demonstrate that the exemplified qubit and qutrit states can be reconstructed with the fidelities 0.952 and 0.961, respectively. Our proposal could be straightforwardly extended to other high-dimensional quantum systems provided that their MUBs exist.

The photonic platform has emerged as a preferred choice for quantum computing and information processing due to its low loss and high integration capabilities. In the present research, we propose a high-dimensional double Feynman gate utilizing single-photon hybrid degrees of freedom coding. This gate can manipulate two qubits simultaneously, demonstrating effective quantum state conversion. Our experimental design offers valuable insights for the investigation of high-dimensional optical quantum logic gates and advances quantum fundamental research.