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Journal of the Optical Society of America B

Ping-pong protocol based on the orbital angular momentum of light

Farnaz Farman, Sara Tofighi, Alireza Bahrampour

Published Sep 4, 2018• 6 citations
Publisher

Abstract

Orbital angular momentum (OAM) is one of the photon’s degrees of freedom in infinite-dimensional Hilbert space. In this paper, we use this photon property to propose a modified version of the deterministic two-way quantum key distribution protocol, known as ping-pong protocol, based on the OAM of light. The advantage of the protocol is that it does not require Bell measurement for decoding the information being transmitted, which makes the protocol more flexible and feasible for practical applications. We propose an implementation setup and show how the channel capacity of the protocol can be easily increased. The security of the protocol is analyzed and the probability of detecting Eve in a general incoherent attack is obtained.

DOI
10.1364/josab.35.002348

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Orbital angular momentum (OAM) is one of the photon’s degrees of freedom in infinite-dimensional Hilbert space. In this paper, we use this photon property to propose a modified version of the deterministic two-way quantum key distribution protocol, known as ping-pong protocol, based on the OAM of light. The advantage of the protocol is that it does not require Bell measurement for decoding the information being transmitted, which makes the protocol more flexible and feasible for practical applications. We propose an implementation setup and show how the channel capacity of the protocol can be easily increased. The security of the protocol is analyzed and the probability of detecting Eve in a general incoherent attack is obtained.
Ping-Pong quantum communication protocol may be employed to transmit deterministically information, so it has instrigued mang researchers. However, there are drawbacks on the security due to the symmetry of the employed two-way quantum channel. In this paper we propose a new attack strategy to eavesdrop the initially transmitted information based on the techniques of quantum error correction code (QECC). In addition, an attack strategy of Ping-Pong scheme based either entanglement state or nonorthogonal state is proofed and demonstrated, respectively. Furthermore, information obtained by Eve and the possible probability detected by the legitimate communicators are analyzed by employing information theorems. Detail proofs and analysis illustrate all previous Ping-Pong quantum communication schemes are insecure, i.e., the eavesdropper may obtain all available information without being detected.
We introduce an attack scheme for eavesdropping freely the ping-pong quantum communication protocol proposed by Boström and Felbinger [ Phys. Rev. Lett. 89 , 187902 (2002)] in a noise channel. The vicious eavesdropper, Eve, intercepts and measures the travel photon transmitted between the sender and the receiver. Then she replaces the quantum signal with a multi-photon signal in the same state, and measures the returned photons with the measuring basis, with which Eve prepares the fake signal except for one photon. This attack increases neither the quantum channel losses nor the error rate in the sampling instances for eavesdropping check. It works for eavesdropping the secret message transmitted with the ping-pong protocol. Finally, we propose a way for improving the security of the ping-pong protocol.
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 deterministic quantum communication protocol, called the ping-pong protocol, has been represented by Boström and Felbinger [Phys. Rev. Lett. 89 (2002) 187902]. Based on an entangled pair of photons, it allows asymptotically secure key distribution and quasi-secure direct communication. However, it was concluded from our previous research that the experiment realization of this protocol requires two optic paths strictly equivalent for interferometry. Here we propose an improved protocol, which is more flexible and secure for conceivable applications. Its feasibility and security are also discussed.
Orbital angular momentum (OAM) states of photons span a high-dimensional Hilbert space, and by using it, higher information capacity and enhanced security can be achieved for both classical communication and quantum key distribution. In this work, we propose a feasible basis-independent encoding scheme for OAM states and show its application in high-dimensional quantum secure direct communication, which enables direct transmission of meaningful messages, in addition to random secret key establishing. Imperfections of optical components may reduce the efficiency of the encoding scheme and, thus, the channel capacity. We discuss the optimal input distribution under realistic conditions to achieve maximal mutual information and an alternative solution using a different set of mutually unbiased bases in the case of a prime-dimensional quantum system.