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arXiv:2608.19945

Entangling two qudits of arbitrary dimension through light-atomic Faraday interaction

R. Surmay, V. A. Leonov, E. A. Vashukevich

quant-phSubmitted Aug 20, 2026• Announced Aug 21, 2026• 0 citations
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Abstract

The paper investigates entangling operations acting on two qudits of arbitrary dimension, with one encoded in the states of a spatially multimode optical field, the other in those of atomic collective spin coherence, both carrying orbital angular momentum (OAM). We demonstrate the generation of a wide range of entangling operations within a protocol consisting of two Faraday interactions and a rotation of atomic and light quadratures between them. All generated gates can be represented as rational powers of the d-dimensional gate $SWAP^α_d$. The probabilities of two-qudit transformations are calculated for various dimensions of the logical space and for different entangling powers of the logical gates.

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arXiv:2106.11046•EPJ Quantum Technology•Aug 17, 2022•1 citation
The paper investigates entangling operations acting on two qudits of arbitrary dimension, with one encoded in the states of a spatially multimode optical field, the other in those of atomic collective spin coherence, both carrying orbital angular momentum (OAM). We demonstrate the generation of a wide range of entangling operations within a protocol consisting of two Faraday interactions and a rotation of atomic and light quadratures between them. All generated gates can be represented as rational powers of the d-dimensional gate SWAPdαSWAP^α_dSWAPdα​. The probabilities of two-qudit transformations are calculated for various dimensions of the logical space and for different entangling powers of the logical gates.
The paper presents an analysis of entangling and nonlocal operations in a quantum nondemolition (QND) interaction between multimode light with orbital angular momentum and an atomic ensemble. A protocol consists of two QND operations with rotations of quadratures of atomic spin coherence and light between them. This protocol provides a wide range of two-qubit operations, while the multimode nature of the chosen degrees of freedom allows the implementation of parallel operations over multiple two-qubit systems. We have used the formalism of equivalence classes and local invariants to evaluate the properties of two-qubit transformations. It is shown that, when selecting suitable values of the governing parameters, such as the duration of each of the two QND interactions and the rotation angles of the qubits, the protocol allows to realize a deterministic nonlocal SWAP operation and entangling SWAP\sqrt{\text{SWAP}}SWAP​ operation with probability 13\frac{1}{3}31​.
Abstract 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 (OAM). Method for logical qudits encoding, which ensures the quasi-cyclicity of operations, is introduced. Based on the protocol for converting the OAM of light in the Raman quantum memory scheme (Vashukevich et al 2020 Phys. Rev. A 101 033830), we show that the considered gates provide an extremely high level of fidelity of single-qudit transformations. We also compare quantum gates’ properties for systems of different dimensions and find the optimal conditions for carrying out transformations in the protocol under consideration.
Nowadays, the quantum swap gate has become an integral part of quantum computing, so the investigation of methods for its realization seems to be an important practical problem for various quantum-optical and information applications. In the present paper, we propose a scheme for performing a swap logic operation in discrete variables in the framework of quantum nondemolition interaction between an atomic ensemble and a multimode light with orbital angular momentum. We discuss in detail the procedure for revealing two-qubit closed subsystems on a set of atomic and field states for different values of the driving field orbital momentum. We also demonstrate the possibility of implementing a parallel multi-two-qubit quantum swap gate.
It has been widely recognized that the underlying principles of quantum mechanics could be used to enable secure communications, without any additional conventional cryptographic systems, while utilizing the properties of the photons. Considerable research efforts have been invested to develop an efficient quantum key distribution (QKD) scheme over either free-space optical or fiber-optics channels. Most of these research efforts have been focused on a two-dimensional QKD, commonly realized by the use of the polarization state of photons. However, the data rates for the quantum key exchange in two-dimensional QKD are still low, while transmission distance is limited. On the other hand, it is well known that photons can carry both the spin angular momentum (SAM) and the orbital angular momentum (OAM), associated with the polarization and azimuthal phase of the complex electric field, respectively. Accordingly, we can define the combined-OAM-SAM state of a photon as |l, σ〉, where l and σ correspond to OAM and SAM indexes, respectively. Since the OAM eigenstates are orthogonal, an arbitrary number of bits per single photon can be transmitted, which could considerably increase the total secure bit rate. To improve secure data rates, we propose two types of protocols, namely, nonentangled-based (such as weak coherent state) and entanglement-assisted protocols, both employing the photon combined-OAM-SAM state, which can be used for secure key distribution over free-space optical and few-mode fiber channels. Two types of entanglement-assisted protocols are described, namely, two-basis and (D + 1)-basis protocols ( D is dimensionality of corresponding Hilbert space). We further describe how to implement the qudit gates required for implementation of these protocols. Finally, we discuss the security issues of the proposed protocols and determine both infinite and finite secret key fraction rates.
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 deterministic arbitrary high-dimensional Pauli XXX gates for single photons carrying orbital angular momentum. The XXX gate consists of a cyclic permutation of qudit basis vectors and, together with the ZZZ gate, forms the basis for performing arbitrary transformations. The proposed experimental setups only use two basic optical elements such as mode sorters and mode shifters and thus could be implemented in any system where these experimental tools are available. Furthermore the number of involved interferometers scales logarithmically with the dimension, which is important for practical implementation.
Abstract 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 savings of resources. The presented schemes utilize only conventional optical elements and apply not only to single photons but also to classical light.