In this paper, we propose several FBG-based both weak coherent state and entanglement assisted multidimensional QKD (MQKD) protocols with mutually unbiased bases (MUBs) derived from the complex Hadamard matrices. We also propose how to implement them by using FBGs with orthogonal impulse responses. The proposed MQKD protocols significantly outperform the conventional two-base QKD protocols, and impose less stringent bandwidth requirements compared to multidimensional time-frequency (t–f) protocols. The proposed FBG-based protocols are capable of simultaneously achieving unprecedented spectral efficiency and secret-key rates (SKRs) in long-distance quantum communication.
In this paper, we propose several FBG-based both weak coherent state and entanglement assisted multidimensional QKD (MQKD) protocols with mutually unbiased bases (MUBs) derived from the complex Hadamard matrices. We also propose how to implement them by using FBGs with orthogonal impulse responses. The proposed MQKD protocols significantly outperform the conventional two-base QKD protocols, and impose less stringent bandwidth requirements compared to multidimensional time-frequency (t–f) protocols. The proposed FBG-based protocols are capable of simultaneously achieving unprecedented spectral efficiency and secret-key rates (SKRs) in long-distance quantum communication.
In this paper, we propose several fiber Bragg gratings (FBGs) based on both weak coherent state (WCS) and entanglement-assisted (EA) multidimensional QKD (MQKD) protocols with mutually unbiased bases (MUBs) derived from the complex Hadamard matrices. We also propose how to implement them by using FBGs with orthogonal impulse responses, derived from Slepian sequences. The proposed FBG-based protocols are capable of simultaneously achieving unprecedented spectral efficiency and secret-key rates in long-distance quantum communication. Regarding the WCS protocols, random base selection and FGB-MUB-based protocols are introduced. Regarding EA protocols, we introduce a generic class of FBG-based N-dimensional protocols and describe the corresponding FBG-based encoders and decoders. The security analysis of the proposed MQKD protocols is further performed by taking into account FBG fabrication imperfections, modeled by the L-neighbor model. It has been shown that the proposed MQKD protocols significantly outperform the conventional two-dimensional QKD protocols, and impose less stringent bandwidth requirements compared to multidimensional time-frequency and time-bin protocols.
In this paper, we propose several entanglement assisted QKD protocols based on time-energy encoding with the number of mutually unbiased bases (MUBs) larger than two. We describe how to implement these protocols based on: (i) optical FFT device implemented in integrated optics with the help of Franson interferometers and (ii) Weyl gate. We also describe the corresponding weak-coherent state-based protocol. By employing the N-dimensional pulse position modulation (ND-PPM) approach, the secret key rate of single photon pulse per signaling interval protocols can be improved by N/log2N times. However, the corresponding entanglement assisted protocols require the use of cavity quantum electrodynamics (CQED) principles to further entangle single photon pulse per frame state. We then analyze the security of the proposed protocols and provide the finite secret key rates in the presence of various imperfections including background errors and timing jitter, for which we propose the K-neighbor model. Finally, we provide the improvements in secret key rates of proposed protocol over conventional two-base time-energy QKD 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.
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.
In majority of protocols of secure quantum communication (such as, BB84, B92, etc.), the unconditional security of the protocols are obtained by using conjugate coding (two or more mutually unbiased bases (MUBs)). Initially, all the conjugate-coding-based protocols of secure quantum communication were restricted to quantum key distribution (QKD), but later on they were extended to other cryptographic tasks (such as, secure direct quantum communication and quantum key agreement). In contrast to the conjugate-coding-based protocols, a few completely orthogonal-state-based protocols of unconditionally secure QKD (such as, Goldenberg–Vaidman and N09) were also proposed. However, till the recent past, orthogonal-state-based protocols were only a theoretical concept and were limited to QKD. Only recently, orthogonal-state-based protocols of QKD are experimentally realized and extended to cryptographic tasks beyond QKD. This paper aims to briefly review the orthogonal-state-based protocols of secure quantum communication that are recently introduced by our group and other researchers.
Quantum key distribution (QKD) protocols based on higher order maximally unbiased bases (MUBs), potentially displaying improved range-security performance, are optically realized for higher (>2) dimensions and/or for multiple (>2) transmission and detection bases, inspired by analogies with the differential phase shift keying and pulse position modulation (PPM) formats of classical optical communication. In particular, we introduce optical realizations for: 1) a six-state protocol in qubit space, employing an extra phase modulated interferometer in the transmitter, detecting the photon in the PPM basis of three consecutive time slots and 2) a 16-state MUB protocol in four dimensions, based on differential phase encoding over four adjacent time slots. The transmitter (Alice) and receiver (Bob) for this system are realized using generalized Mach-Zehnder interferometers with four delay arms, and three phase modulators, further requiring a quantum Hadamard-4 gate, realized using four cross-connected directional couplers, to be implemented as an integrated-optical circuit. The conception and analysis of these optical realizations of abstract higher order QKD MUB-based protocols is inspired by a novel insight into the structure of the MUB set constructed by modulating a generator matrix (typically a Hadamard matrix) with a set of phasemasks. The operating characteristics of these generalized protocols are derived in terms of three simple figures of merit, the Eve detect (or Disturbance) rate, the Eve information rate, and the key creation rate.