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arXiv:2106.11046 · EPJ Quantum Technology

Arbitrary unitaries in orbital angular momentum of single photons

Jaroslav Kysela

Published Aug 17, 2022• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.1140/epjqt/s40507-022-00142-1

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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.
Local quantum gates represent the basic building blocks of quantum computers. In the photonic domain, these gates act on individual photons and are usually implemented as single optical devices. In cases when the same gate is to be applied simultaneously to multiple photons, the corresponding physical implementation consists of a stack of identical devices. We present a systematic approach that allows one to replace this stack with a single device supplemented by pre- and post-processing stages. As a result, considerable savings in resources are obtained. We exemplify our scheme for the case of the orbital angular momentum (OAM) of single photons and demonstrate the scheme for high-dimensional Pauli gates and their arbitrary powers. As a byproduct, we also present a simple argument that explicitly shows how to construct an arbitrary quantum gate acting on OAM of single photons, where only conventional optical elements are utilized.
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Abstract High‐dimensional quantum systems offer many advantages over low‐dimensional quantum systems. Meanwhile, unitary transformations on quantum states are important parts in various quantum information tasks, whereas they become technically infeasible as the dimensionality increases. The photonic orbital angular momentum (OAM), which is inherent in the transverse spatial mode of photons, offers a natural carrier to encode information in high‐dimensional spaces. However, it is even more challenging to realize arbitrary unitary transformations on the photonic OAM states. Here, by combining the path and OAM degrees of freedom of a single photon, an efficient scheme to realize arbitrary unitary transformations on the path‐OAM coupled quantum states is proposed. The proposal reduces the number of required interferometers by approximately one quarter compared with previous works, while maintaining the symmetric structure. It is shown that by using OAM‐to‐path interfaces, this scheme can be utilized to realize arbitrary unitary transformations on the OAM states of photons. This work facilitates the development of high‐dimension quantum state transformations and opens a new door to the manipulation of the photonic OAM states.
The orbital angular momentum (OAM) of photons offers a suitable support to carry the quantum data of multiple users. We present two optical setups that send the information of nnn quantum communication parties through the same free-space optical link. Those qubits can be sent simultaneously and share path, wavelength, and polarization without interference, increasing the communication capacity of the system. The first solution, a qubit combiner, merges nnn channels into the same link, which transmits nnn independent photons. The second solution, the OAM multiplexer, uses controlled-not (CNOT\mathrm{CNOT}CNOT) gates to transfer the information of nnn optical channels to a single photon. Additional applications of the multiplexer circuits, such as quantum arithmetic, as well as connections to OAM sorting are discussed.
Structured light carrying Orbital Angular Momentum (OAM) enables high-dimensional photonic quantum information processing. In this work, we propose and theoretically demonstrate a four-dimensional controlledNOT (CNOT) quantum gate implemented using the radial (p) and azimuthal (l) degrees of freedom of Laguerre–Gaussian modes. Quantum information is encoded within a single photon, with the radial mode acting as the control qubit and the OAM mode as the target qubit. The gate is realized using fully linear and unitary optical transformations based on Fourier transform based radial mode sorting and OAM inversion within the architecture. This approach enables deterministic two-qubit logic in an expanded Hilbert space, providing a scalable pathway toward high-dimensional quantum gates using structured light.