© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Laser & Photonics Review

Toward Universal Transformations of Orbital Angular Momentum of a Single Photon

Dong‐Xu Chen, Yunlong Wang, Feiran Wang, Jun‐Long Zhao, Chui‐Ping Yang

Published May 9, 2023• 3 citations

Abstract

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.

DOI: 10.1002/lpor.202300277

Related papers

Fourier Transform of the Orbital Angular Momentum of a Single Photon

Jaroslav Kysela, Xiaoqin Gao, Borivoje Dakić

Optical networks implementing single-qudit quantum gates may exhibit superior properties to those for qubits as each optical element in the network can work in parallel on many optical modes simultaneously. We present a class of such networks that implements in a deterministic and efficient way the quantum Fourier transform (QFT) in an arbitrarily high dimension. These networks redistribute the initial quantum state into the orbital angular momentum (OAM) and path degrees of freedom and offer two modes of operation. Either the OAM-only QFT can be implemented, which uses the path as an internal auxiliary degree of freedom, or the path-only QFT is implemented, which uses the OAM as the auxiliary degree of freedom. The resources for both schemes scale linearly $O(d)$ with the dimension $d$ of the system, beating the best known bounds for the path-encoded QFT. While the QFT of the orbital-angular-momentum states of single photons has been applied in a multitude of experiments, these schemes require specially designed elements with nontrivial phase profiles. In contrast, we propose a different approach that utilizes only conventional optical elements.

arXiv:2004.12788•Physical Review Applied•Sep 14, 2020•15 citations

Universal unitary gate for single-photon spin-orbit four-dimensional states

Sergei Slussarenko, Ebrahim Karimi, Bruno Piccirillo +2 more

The recently demonstrated possibility of entangling opposite values of the orbital angular momentum (OAM) of a photon with its spin enables the realization of nontrivial one-photon spin-orbit four-dimensional states for quantum information purposes. Hitherto, however, an optical device that can able to perform arbitrary unitary transformations on such spin-orbit photon states has not been proposed yet. In this work we show how to realize such a ``universal unitary gate'' device, based only on the existing optical technology, and describe its operation. Besides the quantum information field, the proposed device may find applications wherever an efficient and convenient manipulation of the combined OAM and spin of light is required.

arXiv:0906.3989•Physical Review A•Aug 21, 2009•22 citations

Cyclic transformation of orbital angular momentum modes

Florian Schlederer, Mario Krenn, Robert Fickler +2 more

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-fold cyclic transformation of OAM modes. Interestingly, our experimental setup was found by a computer algorithm. In addition to the four-cyclic transformation, the algorithm also found extensions to higher-dimensional cycles in a hybrid space of OAM and polarization. Besides being useful for quantum cryptography with QuDits, cyclic transformations are key for the experimental production of high-dimensional maximally entangled Bell-states.

arXiv:1512.02696•New Journal of Physics•Apr 14, 2016•48 citations

Engineering of photonic orbital angular momentum quantum states for quantum information processing

Eleonora Nagali, Lorenzo Marrucci, Enrico Santamato +1 more

Among all degrees of freedom offered by single photons, the orbital angular momentum (OAM) has a great potential in the quantum information field, as it provides a natural choice for implementing single-photon qudits, the units of quantum information in a higher dimensional space. This can be an important practical advantage, as it enables higher security in quantum cryptographic protocols, as well as implications in fundamental quantum mechanics theory. Moreover, the combined use of different degrees of freedom of a photon, such as OAM and spin, enables the implementation of entirely new quantum tasks.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•May 1, 2011•0 citations

Entanglement of very high orbital angular momentum

Robert Fickler, Peizhe Li, Radek Łapkiewicz +5 more

Orbital angular momentum (OAM) of single photons represents a new optical degree of freedom for the entanglement of photons [1,2]. One physical realization of OAM carrying light beams are the so called Laguerre-Gaussian modes of light with the required helical phase structure. One big advantage over the well known polarization degree of freedom is the possibility of realizing entanglement between two photons with very high quantum numbers. However, the creation of photonic OAM entanglement using the widely used spontaneous parametric downconversion process is limited by the strongly reduced efficiency for higher momenta [3]. We have realized a novel method to create entanglement between two photons with a very high difference in their OAM quantum number and momentum respectively. Furthermore we have explored hybrid entanglement of photons in the OAM and polarization degree of freedom.

Frontiers in Optics•Jan 1, 2011•1 citation

Scalable cyclic transformation of orbital angular momentum modes based on a nonreciprocal Mach–Zehnder interferometer

Yu-Fang Yang, Mingyuan Chen, Feng-Pei Li +5 more

The orbital angular momentum (OAM) of photons provides a pivotal resource for carrying out high-dimensional classical and quantum information processing due to its unique discrete high-dimensional nature. The cyclic transformation of a set of orthogonal OAM modes is an essential building block for universal high-dimensional information processing. Its realization in the quantum domain is the universal quantum Pauli-X gate. In this work, we experimentally demonstrate a cyclic transformation of six OAM modes with an averaged efficiency higher than 96% by exploiting a nonreciprocal Mach–Zehnder interferometer. Our system is simple and can, in principle, be scaled to more modes. By improving phase stabilization and inputting quantum photonic states, this method can perform universal single-photon quantum Pauli-X gate, thus paving the way for scalable high-dimensional quantum computation.

arXiv:2404.14690•Photonics Research•Jul 29, 2024•1 citation

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.

Optical networks implementing single-qudit quantum gates may exhibit superior properties to those for qubits as each optical element in the network can work in parallel on many optical modes simultaneously. We present a class of such networks that implements in a deterministic and efficient way the quantum Fourier transform (QFT) in an arbitrarily high dimension. These networks redistribute the initial quantum state into the orbital angular momentum (OAM) and path degrees of freedom and offer two modes of operation. Either the OAM-only QFT can be implemented, which uses the path as an internal auxiliary degree of freedom, or the path-only QFT is implemented, which uses the OAM as the auxiliary degree of freedom. The resources for both schemes scale linearly

O(d)

with the dimension

d

of the system, beating the best known bounds for the path-encoded QFT. While the QFT of the orbital-angular-momentum states of single photons has been applied in a multitude of experiments, these schemes require specially designed elements with nontrivial phase profiles. In contrast, we propose a different approach that utilizes only conventional optical elements.

The recently demonstrated possibility of entangling opposite values of the orbital angular momentum (OAM) of a photon with its spin enables the realization of nontrivial one-photon spin-orbit four-dimensional states for quantum information purposes. Hitherto, however, an optical device that can able to perform arbitrary unitary transformations on such spin-orbit photon states has not been proposed yet. In this work we show how to realize such a ``universal unitary gate'' device, based only on the existing optical technology, and describe its operation. Besides the quantum information field, the proposed device may find applications wherever an efficient and convenient manipulation of the combined OAM and spin of light is required.

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-fold cyclic transformation of OAM modes. Interestingly, our experimental setup was found by a computer algorithm. In addition to the four-cyclic transformation, the algorithm also found extensions to higher-dimensional cycles in a hybrid space of OAM and polarization. Besides being useful for quantum cryptography with QuDits, cyclic transformations are key for the experimental production of high-dimensional maximally entangled Bell-states.

Among all degrees of freedom offered by single photons, the orbital angular momentum (OAM) has a great potential in the quantum information field, as it provides a natural choice for implementing single-photon qudits, the units of quantum information in a higher dimensional space. This can be an important practical advantage, as it enables higher security in quantum cryptographic protocols, as well as implications in fundamental quantum mechanics theory. Moreover, the combined use of different degrees of freedom of a photon, such as OAM and spin, enables the implementation of entirely new quantum tasks.

Orbital angular momentum (OAM) of single photons represents a new optical degree of freedom for the entanglement of photons [1,2]. One physical realization of OAM carrying light beams are the so called Laguerre-Gaussian modes of light with the required helical phase structure. One big advantage over the well known polarization degree of freedom is the possibility of realizing entanglement between two photons with very high quantum numbers. However, the creation of photonic OAM entanglement using the widely used spontaneous parametric downconversion process is limited by the strongly reduced efficiency for higher momenta [3]. We have realized a novel method to create entanglement between two photons with a very high difference in their OAM quantum number and momentum respectively. Furthermore we have explored hybrid entanglement of photons in the OAM and polarization degree of freedom.

The orbital angular momentum (OAM) of photons provides a pivotal resource for carrying out high-dimensional classical and quantum information processing due to its unique discrete high-dimensional nature. The cyclic transformation of a set of orthogonal OAM modes is an essential building block for universal high-dimensional information processing. Its realization in the quantum domain is the universal quantum Pauli-X gate. In this work, we experimentally demonstrate a cyclic transformation of six OAM modes with an averaged efficiency higher than 96% by exploiting a nonreciprocal Mach–Zehnder interferometer. Our system is simple and can, in principle, be scaled to more modes. By improving phase stabilization and inputting quantum photonic states, this method can perform universal single-photon quantum Pauli-X gate, thus paving the way for scalable high-dimensional quantum computation.