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Nanosystems Physics Chemistry Mathematics

Pulsed phase modulation with harmonic electric control signal for quantum key distribution implementations

Andrei Gaidash, George P. Miroshnichenko, Козубов Антон Владимирович

Published Mar 4, 2026• 1 citation
Publisher

Abstract

In this work, we investigate an alternative approach to phase modulation for information encoding and decoding in quantum key distribution systems. Specifically, we propose pulsed phase modulation, i.e. it has an envelope in addition to previously considered only harmonic temporal behavior of modulation index (depth), as a replacement for the conventional use of both intensity and phase modulators, which enables a more compact and cost-effective optical design. We further analyze how the principal parameters of this scheme affect the interference observed at the receiver and, consequently, their contribution to the quantum bit error rate in a subcarrier-wave quantum key distribution implementation.

DOI
10.17586/2220-8054-2026-17-1-39-45

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In this work, we investigate an alternative approach to phase modulation for information encoding and decoding in quantum key distribution systems. Specifically, we propose pulsed phase modulation, i.e. it has an envelope in addition to previously considered only harmonic temporal behavior of modulation index (depth), as a replacement for the conventional use of both intensity and phase modulators, which enables a more compact and cost-effective optical design. We further analyze how the principal parameters of this scheme affect the interference observed at the receiver and, consequently, their contribution to the quantum bit error rate in a subcarrier-wave quantum key distribution implementation.
Quantum key distribution (QKD) allows secret key exchange between two users with unconditional security. For QKD to be widely deployed, low cost and compactness are crucial requirements alongside high performance. Currently, the majority of QKD systems demonstrated rely on bulk intensity and phase modulators to generate optical pulses with precisely defined amplitude and relative phase difference—i.e., to encode information as signal states and decoy states. However, these modulators are expensive and bulky, thereby limiting the compactness of QKD systems. Here, we present and experimentally demonstrate a novel optical transmitter design to overcome this disadvantage by generating intensity- and phase-tunable pulses at GHz clock speeds. Our design removes the need for bulk modulators by employing directly modulated lasers in combination with optical injection locking and coherent interference. This scheme is, therefore, well suited to miniaturization and photonic integration, and we implement a proof-of-principle QKD demonstration to highlight potential applications.
Quantum key distribution provides a promising solution for sharing secure keys between two distant parties with unconditional security. Nevertheless, quantum key distribution is still severely threatened by the imperfections of devices. In particular, the classical pulse correlation threatens security when sending decoy states. To address this problem and simplify experimental requirements, we propose a phase-matching quantum key distribution protocol without intensity modulation. Instead of using decoy states, we propose an alternative method to estimate the theoretical upper bound on the phase error rate contributed by even-photon-number components. Simulation results show that the transmission distance of our protocol could reach 305 km in telecommunication fiber. Furthermore, we perform a proof-of-principle experiment to demonstrate the feasibility of our protocol, and the key rate reaches 22.5 bit/s under a 45-dB channel loss. Addressing the security loophole of pulse intensity correlation and replacing continuous random phase with a six- or eight-slice random phase, our protocol provides a promising solution for constructing quantum networks.
This paper presents novel quantum key distribution (QKD) schemes that use differential phases of sequential pulses as an information carrier. Alice sends a photon in a linear superposition state of three temporal slots, in which each amplitude is phase-modulated by {0,π}. Bob measures the phase difference of an asymmetric interferometer, and tells Alice time-instance at which the photon was counted. From this time information and her modulation data, Alice knows which detector counted the photon in Bob s site. Then, the two parties create a secret key. The scheme is suitable for fiber transmission systems and offers key creation efficiency higher than conventional phase-encoding QKD. The above scheme utilizes fully non-orthogonal four states. Differential phase shift QKD utilizing two non-orthogonal states is also presented. Alice sends a coherent pulse train with less than one photon per pulse, which is phase modulated by {0,π} for each pulse, and Bob measures the pulse train by a one-bit delay circuit. The system has a simple configuration such that Alice has no interferometer and sends no intense reference pulse, unlike to conventional QKD scheme using two non-orthogonal states, and also has an advantage of high key creation efficiency.
Major progress in quantum key distribution (QKD) has been realised recently both for free space and fiber implementations. For advanced QKD systems over fiber, information is encoded in the relative phase between delayed pulses or in polarization. Recently, we proposed an alternative approach where optical pulses are weakly modulated to generate spectral domain sidebands about a central peak. The information is encoded by the relative phase between the sidebands and the central peak. In this paper, we propose a modified architecture based on phase encoding with active dispersion compensation at 12.5 GHz that potentially allows the use of a high bit rate clock.