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International Conference on Transparent Optical Networks

Photon angular momentum based multidimensional quantum key distribution

Ivan B. Djordjević, Yequn Zhang

Published Jul 1, 2014• 1 citation
Publisher

Abstract

In this invited paper, we describe the photon angular momentum based entanglement assisted quantum key distribution (QKD) protocols, analyse their security, and determine the secure finite key fraction rates. Two types of entanglement-assisted protocols, namely two-basis and (D+1)-basis protocols (D is dimensionality of corresponding Hilbert space), have been identified as the most promising. We further analyse the implementation of the qubit gates required for these protocols. We demonstrate that photon angular momentum based QKD protocols significantly outperform corresponding two-dimensional QKD protocols in terms of the finite secret key rates.

DOI
10.1109/icton.2014.6876370

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In this invited paper, we describe the photon angular momentum based entanglement assisted quantum key distribution (QKD) protocols, analyse their security, and determine the secure finite key fraction rates. Two types of entanglement-assisted protocols, namely two-basis and (D+1)-basis protocols (D is dimensionality of corresponding Hilbert space), have been identified as the most promising. We further analyse the implementation of the qubit gates required for these protocols. We demonstrate that photon angular momentum based QKD protocols significantly outperform corresponding two-dimensional QKD protocols in terms of the finite secret key rates.
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.
We present a detailed security analysis of a d -dimensional quantum key distribution protocol based on two and three mutually unbiased bases (MUBs) both in an asymptotic and finite-key-length scenario. The finite secret key rates (in bits per detected photon) are calculated as a function of the length of the sifted key by (i) generalizing the uncertainly relation-based insight from BB84 to any d -level 2-MUB QKD protocol and (ii) by adopting recent advances in the second-order asymptotics for finite block length quantum coding (for both d -level 2- and 3-MUB QKD protocols). Since the finite and asymptotic secret key rates increase with d and the number of MUBs (together with the tolerable threshold) such QKD schemes could in principle offer an important advantage over BB84. We discuss the possibility of an experimental realization of the 3-MUB QKD protocol with the orbital angular momentum degrees of freedom of photons.
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.
We present an experimental study of higher-dimensional quantum key distribution protocols based on mutually unbiased bases, implemented by means of photons carrying orbital angular momentum. We perform (d+1d+1d+1) mutually unbiased measurements in a classically simulated prepare-and-measure scheme and on a pair of entangled photons for dimensions ranging from d=2d=2d=2 to 5. In our analysis, we pay attention to the detection efficiency and photon pair creation probability. As security measures, we determine from experimental data the average error rate, the mutual information shared between the sender and receiver, and the secret key generation rate per photon. We demonstrate that increasing the dimension leads to an increased information capacity as well as higher key generation rates per photon. However, we find that the benefit of increasing the dimension is limited by practical implementation considerations, which in our case results in deleterious effects observed beyond a dimension of d=4d=4d=4.
We propose a schematic setup of quantum key distribution (QKD) with an improved secret key rate based on high-dimensional quantum states. Two degrees-of-freedom of a single photon, orbital angular momentum modes, and multi-path modes, are used to encode secret key information. Its practical implementation consists of optical elements that are within the reach of current technologies such as a multiport interferometer. We show that the proposed feasible protocol has improved the secret key rate with much sophistication compared to the previous 2-dimensional protocol known as the detector-device-independent QKD.
This paper proposes an enhanced Quantum Key Distribution (QKD) protocol by incorporating a Three-Dimensional Angular Momentum Representation (3D AMR) to address vulnerabilities inherent in traditional two-dimensional polarization states-based systems. The 3D AMR method expands the state space, potentially increasing security against sophisticated quantum attacks. We present a theoretical and computational framework that transitions from the conventional two-dimensional polarization to a three-dimensional angular momentum space, which inherently increases the complexity and security of the quantum states used in QKD.