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arXiv:2210.10501 · Laser Physics Letters

Multiqudit quantum hashing and its implementation based on orbital angular momentum encoding

D O Akat’ev, Alexander Vasiliev, N. M. Shafeev, Farid Mansurovich Ablayev, А. А. Калачев

Published Nov 9, 2022• 9 citations
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Abstract

Abstract 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.

DOI
10.1088/1612-202x/ac9ec3

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Abstract 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.
Quantum hashing is a promising generalization of the cryptographic hashing concept on the quantum domain. In this paper, we construct a quantum hash via a sequence of single-photon states and perform a proof-of-principle experiment using orbital angular momentum (OAM) encoding. We experimentally verify the collision resistance of the quantum hash function depending on the number of qubits in use. Based on these results, we conclude that theoretical estimates are confirmed for different bases of OAM states and the proposed technique can be useful in computational and cryptographic scenarios. The possibility of multiplexing different OAM bases can make this approach even more efficient.
Abstract Quantum hashing is one of the techniques that allow to construct space-efficient quantum algorithms and protocols. We present a construction that allows to make it extremely time efficient. Our approach is based on the shallow implementation of the quantum fingerprinting technique but uses additional circuit identities specific to the quantum hash function for the cyclic group. The resulting algorithm is equivalent to the one we have implemented earlier using single-photon states with orbital angular momentum encoding.
Abstract Recently we have proposed an adapted version of the quantum hash function that minimizes quantum state engineering and experimentally verified the collision resistance of such function. The proposed construction describes a quantum hash as a sequence of single-photon states using orbital angular momentum (OAM) encoding that is a promising platform for optical quantum technologies. In this paper we give an existence proof for parameter sets that will guarantee a very high collision resistance for OAM-based quantum hash function.
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.
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.