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National Conference on Communications

Optical modulation schemes for frequency-coded quantum key distribution

Pradeep K Kumar

Published Jan 1, 2010• 7 citations
Publisher

Abstract

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.

DOI
10.1109/ncc.2010.5430155

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2018Systems of Signal Synchronization, Generating and Processing in Telecommunications (SYNCHROINFO)•Jul 1, 2017•3 citations
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.
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 propose a decoy-pulse protocol for frequency-coded implementation of B92 quantum key distribution protocol. A direct extension of decoy-pulse method to frequency-coding scheme results in security loss as an eavesdropper can distinguish between signal and decoy pulses by measuring the carrier photon number without affecting other statistics. We overcome this problem by optimizing the ratio of carrier photon number of decoy-to-signal pulse to be as close to unity as possible. In our method the switching between signal and decoy pulses is achieved by changing the amplitude of RF signal as opposed to modulating the intensity of optical signal thus reducing system cost. Our simulation results show a key generation rate of 1.5×10-4/pulse for link lengths up to 70 km. Finally, we discuss the optimum value of average photon number of signal pulse for a given key rate while also optimizing the carrier ratio.
We describe a frequency-coded scheme to implement the BB84 quantum key distribution protocol using spin wave (SW)-optical interactions. The interaction of SWs with optical coherent states allows TE↔TM mode conversion with simultaneous change of frequency and polarization while introducing a phase difference between the two modes. To implement the BB84 protocol, key bits are encoded as relative phases between the TE and TM modes. The proposed scheme offers a higher key rate, due to a modulation frequency as high as 25 GHz, which also relaxes the specifications on the optical filter at the receiver. In addition, SW-optical interactions yield the added security of truly single-sideband modulation.
We propose the use of spin wave–optical interactions to implement the BB84 and B92 quantum key distribution (QKD) protocols. Spin waves couple the transverse magnetic (TM) and transverse electric (TE) optical modes of a waveguide. We derive the interaction Hamiltonian to describe the coupling, and solve the resulting equations to determine the time evolution of quantized TM and TE modes. With a judicious choice of coupling coefficient, a set of four nonorthogonal states-formally equivalent to the set of polarization states of a single photon-can be generated. These states form a conjugate basis suitable as a QKD basis set. The proposed scheme can mitigate any medium-induced polarization fluctuations. The spin wave–optical interactions can be used to implement the BB84 protocol using frequency-coded coherent optical states.
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.