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Acta Physica Sinica

Study on quantum cryptography using orbital angular momentum states of photons

Zhi-Kun Su, Wang Fa-Qiang, Lu Yi-Qun, Jin Rui-Bo, Liang Ruisheng, Songhao Liu, 华南师范大学信息光电子科技学院,光子信息技术广东省高校重点实验室,广州 510006

Published Jan 1, 2008• 5 citations
Publisher

Abstract

We present a simple quantum cryptographic scheme that encodes information in two orthogonal orbital angular momentum states. The states used in this scheme are invariant under rotations of the propagation direction,making this implementation independent of the alignment between the reference frames of Alice and Bob. Besides,since the two orbital angular momentum states are orthogonal,100% use of the photons is attained,which increases the key generation rate of the protocol.

DOI
10.7498/aps.57.3016

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We present a simple quantum cryptographic scheme that encodes information in two orthogonal orbital angular momentum states. The states used in this scheme are invariant under rotations of the propagation direction,making this implementation independent of the alignment between the reference frames of Alice and Bob. Besides,since the two orbital angular momentum states are orthogonal,100% use of the photons is attained,which increases the key generation rate of the protocol.
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The existing quantum secure direct communication (QSDC) protocols mainly make use of the spin angular momentum and entangled photons, to realize direct transmission of confidential information. But those protocols' capacity is low, only one-bit information. On the other hand, the orbital angular momentum (OAM) of a photon can be theoretically evaluated from minus infinity to infinity, and the angular momentum states of different orbits are orthogonal to each other. Given that, in this paper, we propose a quantum secure direct communication scheme based on OAM. Specifically, taking OAM of photons as the information carrier, the data of information is segmented and high-capacity coding in quantum secure direct communication is realized through the segmentation of sector states.
We experimentally demonstrate a quantum key distribution protocol using entangled photon pairs in orbital angular momentum (OAM). Here Alice uses a fixed phase hologram to modulate her OAM state on one photon with a spatial light modulator (SLM), while Bob uses the designed N different phase holograms for his N-based keys on the other photon with his SLM. With coincidences, Alice can fully retrieve the keys sent by Bob without reconciliation. We report the experiment results with N = 3 and OAM eigenmodes |ℓ = ±1〉, and discuss the security from the light path and typical attacks.
The nondiffracting higher-order Bessel beams carry the orbital angular momentum(OAM). During free propagation,their transverse intensity profile remains nearly invariant in a range.The beam comprises the topological charge l helical phasefronts and carries an orbital angular momentum of lh per photon.The angular momentum number carried by the photon in each eigenmode is represented by l, and the eigenstates |l〉can generate multidimensional quantum entangled states.A method of optical communication is presented that encodes information in two orthogonal orbital angular momentum states based on higher-order Bessel beams.Each photon carries OAM states of information,which can increase the key generation rate of the protocol,and offer a quantum solution for increase of the optical communication distance.
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.
A new implementation of high-dimensional quantum key distribution (QKD) protocol is discussed. Using three mutual unbiased bases, we present a d-level six-state QKD protocol that exploits the orbital angular momentum with the spatial mode of the light beam. The protocol shows that the feature of a high capacity since keys are encoded using photon modes in d-level Hilbert space. The devices for state preparation and measurement are also discussed. This protocol has high security and the alignment of shared reference frames is not needed between sender and receiver.