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SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference (IMOC)

Modulation schemes for frequency coded quantum key distribution

GUILHERME BARRETO XAVIER, Jean Pierre von der Weid

Published Oct 4, 2006• 3 citations
Publisher

Abstract

Frequency coding has been presented as a new alternative for qubits transmission on QKD systems. In this work we present an analysis of the different possibilities for modulation (amplitude or phase) in face of the BB84 and B92 protocols within systems employing frequency coding. It will be shown that schemes employing phase modulation both at Alice and Bob (PM-PM) are equivalent, in the sense that the classical BB84 protocol cannot be applied, to schemes using solely amplitude modulation (AM-AM). We present a new modulation scheme employing a combination of phase and amplitude modulation (AM-PM) which can accommodate classical BB84.

DOI
10.1109/imoc.2005.1580106

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Frequency coding has been presented as a new alternative for qubits transmission on QKD systems. In this work we present an analysis of the different possibilities for modulation (amplitude or phase) in face of the BB84 and B92 protocols within systems employing frequency coding. It will be shown that schemes employing phase modulation both at Alice and Bob (PM-PM) are equivalent, in the sense that the classical BB84 protocol cannot be applied, to schemes using solely amplitude modulation (AM-AM). We present a new modulation scheme employing a combination of phase and amplitude modulation (AM-PM) which can accommodate classical BB84.
We discuss possible modulation schemes to implement BB84 and B92 quantum key distribution protocols using frequency-coding method. We derive time evolution of quantum states of light in a Mach-Zehnder interferometer based optical intensity modulator. We then show that phase modulator-phase modulator (PM-PM) combination can be used to implement the B92 protocol and intensity modulator-intensity modulator (IM-IM) combination can be used to implement the BB84 protocol. However, the combinations-PM-IM or IM-PM-cannot be used to implement BB84 and B92 protocols using frequency-coding method. Finally, we discuss the security of frequency-coded implementation of B92 protocol.
The technology of frequency coding in channels of quantum key distribution allows to determine the ground state of photons through the value of the amplitude of its carrier, frequency modulated in phase (PM) or amplitude (AM) by a radio-frequency signal, and the resulting side components. Over the past twenty years, it has been substantially modified and improved. At the same time, in recent works, an expanded understanding of the frequency coding principle is used, in which each photon state is associated not with the phase of the modulating signal at a certain frequency, but with one or more sideband frequencies or the carrier frequency of the photon itself. The known schemes of electro-optical modulation and remodulation are described by the symmetric pairs PM-PM, AM-AM and AM-PM (PM-AM), where the first component determines the modulator type on the Alice side (legal subscriber - transmitter), and the second one on the side of Bob legal subscriber - receiver). It is noted, that the smallest value of QBER is achieved in schemes with a passive definition of one or two basic states of a photon, i.e. without the use of remodulation processes. The formation of a filter system is carried out using fiber Bragg gratings (FBG) or arrayed waveguide gratings (AWG), tuned to the photon carrier or it sideband components. In this paper, we present the results of constructing a universal system of quantum key distribution (QKD) based on the electro-optical AMPM-PMAM scheme, which makes it possible to realize all the above-mentioned schemes and additionally combined version. At the heart of the AMPMPMAM system of the QKD system is the modulation transformation of the photon carrier based on the Il'inMorozov's method and its one- and two-modulator realizations. For the mathematical description of the scheme, the principles of constructing a single-port modulation microwave photonic link of a sequential type and photon modeling of electro-optical modulators were used. The use of the universal scheme will allow using several levels of cryptographic protection, including switching schemes and protocols, with remodulation and only passive detection. In addition, it should be noted the high spectral efficiency of the Il'in-Morozov's modulation conversion, its spectral purity and the stability of the received characteristics of the output radiation when the conversion parameters deviate from the optimal ones. The possibility of reducing the probability of achieving a positive result in PNS attacks by Eva (illegal subscriber) is shown by eliminating the carrier of the signal transmitted via the quantum channel from the structure of the key distribution.
The technology of frequency coding in channels of quantum key distribution allows to determine the ground state of photons through the value of the amplitude of its carrier, frequency modulated in phase (PM) or amplitude (AM) by a radio-frequency signal, and the resulting side components. Over the past twenty years, it has been substantially modified and improved. At the same time, in recent works, an expanded understanding of the frequency coding principle is used, in which each photon state is associated not with the phase of the modulating signal at a certain frequency, but with one or more sideband frequencies or the carrier frequency of the photon itself. In this paper, we present the results of constructing a frequency coding system of quantum key distribution (QKD) based on the serial electro-optical photon amplitude modulation and phase commutation. The possibility of reducing the probability of achieving a positive result in PNS attacks by Eva is shown by eliminating the carrier of the signal transmitted via the quantum channel from the structure of the key distribution. It was early noted, that the smallest value of QBER is achieved in schemes with a passive definition of one or two basic states of a photon, i.e. without the use of remodulation processes, that is realized in considering. Additionally it is not necessary to form a notch filter system, which is usually carried out using fiber Bragg gratings (FBG) or arrayed waveguide gratings (AWG) for discrimination the photon carrier and its sideband components.
We have theoretically and experimentally address the possible tandem electro-optical modulator configurations that can be employed to implement Frequency Coded Quantum Key Distribution systems (FC-QKD). A closed and general formulation of the end to end field propagation in a dispersion compensated FC-QKD optical fiber system under the low modulation index regime is presented which accounts for all the possible tandem combinations. The properties and the parameter selection of the modulators to achieve each one are summarized. We also address which protocol (B92, BB84 or either) is feasible to be implemented with each configuration. The results confirm those reported for the configurations previously reported in the literature and, at the same time, show the existence of four novel tandem modulator configurations that can also be employed. We have also provided experimental evidence of the successful operation of the novel configurations that confirm the behavior predicted by the theoretical results.