Multidimensional QKD Based on Combined Orbital and Spin Angular Momenta of Photon

Abstract

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 jl; i, where l and 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 ðD þ 1Þ-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.Index Terms: Quantum information processing (QIP), quantum qudit gates, quantum key distribution (QKD), orbital angular momentum (OAM), spin angular momentum (SAM), low-density parity-check (LDPC) codes.

A new designed dual-guided ring-core fiber for OAM mode transmission

“…Although significant advances have been achieved in QKD both for free-space and fiber channel, the secure key rates in two-dimensional QKD are still low and the secure transmission distance is limited. OAM based QKD structure is a promising candidate for the next generation of high-speed QKD system [8,9].…”

Photon angular momentum based multidimensional quantum key distribution

“…By limiting OAM index l to maximum L, the corresponding space is D = 2(2L + 1)-dimensional. Notice that this concept of photon angular momentum states, which can also be called the combined-OAM-SAM photon states [4], is different from the total angular momentum (TAM) of photon defined as j ħ = (l + σ)ħ and introduced in [3]. The number of base kets in TAM representation is 2L + 3, while in |l,σ-representation corresponding number of states is 2(2L + 1).…”

“…For the configuration of D-dimensional OAM modulators, please refer to ref. [4], which is also provided in Fig. 2 for completeness of presentation.…”

“…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 a photon angular momentum of a photon obtained as a combination of SAM and OAM, as we described in [4]. 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.…”

A new designed OAM fiber enabling the integration of classical and quantum optical fiber communications

“…Although significant advances have been made in QKD for both free-space and fiber channel, the secure key rates in two-dimensional QKD are still low and the secure transmission distance is limited. OAM based QKD architecture is a promising candidate for the next generation of high-speed QKD system [3,4].…”