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Optics Express

Shared-reference-frame-independent continuous-variable quantum key distribution

Vladyslav C. Usenko

Published Mar 28, 2025• 3 citations
Publisher

Abstract

The protocol of continuous-variable quantum key distribution based on quadrature modulation of coherent states and heterodyne quadrature detection, which does not rely on sharing either a local oscillator or pilot tones, is proposed. Using unidimensional single-quadrature encoding, we suggest alignment of the measurement bases relying on the asymmetry of the phase-space distribution of the modulated states. By rotating the bases so that the maximum quadrature variance is observed, the remote communicating party can identify the signal quadrature direction. Depending on the coherence time of the signal and the repetition rate of the system, the necessary statistics can be accumulated to minimize misalignment between the preparation and measurement bases. We address the issue of residual bases misalignment in the suggested shared-reference-frame-independent continuous-variable quantum key distribution protocol and show that it is feasible with state-of-the-art techniques. The result paves the way for low-cost and simplified quantum communication schemes, which are independent of any shared phase reference and are therefore immune to potential quantum hacking attacks on the local oscillator or pilot tones.

DOI
10.1364/oe.551996

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The protocol of continuous-variable quantum key distribution based on quadrature modulation of coherent states and heterodyne quadrature detection, which does not rely on sharing either a local oscillator or pilot tones, is proposed. Using unidimensional single-quadrature encoding, we suggest alignment of the measurement bases relying on the asymmetry of the phase-space distribution of the modulated states. By rotating the bases so that the maximum quadrature variance is observed, the remote communicating party can identify the signal quadrature direction. Depending on the coherence time of the signal and the repetition rate of the system, the necessary statistics can be accumulated to minimize misalignment between the preparation and measurement bases. We address the issue of residual bases misalignment in the suggested shared-reference-frame-independent continuous-variable quantum key distribution protocol and show that it is feasible with state-of-the-art techniques. The result paves the way for low-cost and simplified quantum communication schemes, which are independent of any shared phase reference and are therefore immune to potential quantum hacking attacks on the local oscillator or pilot tones.
The possibility of using squeezed states in the recently suggested unidimensional continuous-variable quantum key distribution based on a single quadrature modulation is addressed. It is shown that squeezing of the signal states expands the physicality bounds of the effective entangled state shared between the trusted parties due to the antisqueezing noise in the unmodulated quadrature. Modulation of the antisqueezed quadrature, on the other hand, effectively shrinks the physicality bounds due to the squeezing in the unmodulated quadrature and also provides noise on the reference side of the protocol, thus limiting the possibility of eavesdropping in noisy channels. This strategy is practical for low-loss (i.e., short-distance) channels, especially if direct reconciliation scheme is applied.
Most continuous-variable quantum key distribution schemes are based on the Gaussian modulation of coherent states followed by continuous quadrature detection using homodyne detectors. In all previous schemes, the Gaussian modulation has been carried out in conjugate quadratures thus requiring two independent modulators for their implementations. Here, we propose and experimentally test a largely simplified scheme in which the Gaussian modulation is performed in a single quadrature. The scheme is shown to be asymptotically secure against collective attacks, and considers a specific attack using asymmetric preparation and excess noise. We find that this protocol is considerably more sensitive to noise than other CVQKD schemes, as a consequence of the simplified implementation. A single-quadrature modulation approach renders the need for a costly amplitude modulator unnecessary, and thus facilitates commercialization of continuous-variable quantum key distribution, provided that the low noise requirement can be achieved.
A high-speed Gaussian-modulated continuous-variable quantum key distribution (CVQKD) with a local local oscillator (LLO) is experimentally demonstrated based on pilot-tone-assisted phase compensation. In the proposed scheme, the frequency-multiplexing and polarization-multiplexing techniques are used for the separate transmission and heterodyne detection between quantum signal and pilot tone, guaranteeing no crosstalk from strong pilot tone to weak quantum signal and different detection requirements of low-noise for quantum signal and high-saturation limitation for pilot tone. Moreover, compared with the conventional CVQKD based on homodyne detection, the proposed LLO-CVQKD scheme can measure X and P quadrature simultaneously using heterodyne detection without need of extra random basis selection. Besides, the phase noise, which contains the fast-drift phase noise due to the relative phase of two independent lasers and the slow-drift phase noise introduced by quantum channel disturbance, has been compensated experimentally in real time, so that a low level of excess noise with a 25 km optical fiber channel (with 5 dB loss) is obtained for the achievable secure key rate of 7.04 Mbps in the asymptotic regime and 1.85 Mbps under the finite-size block of 107.
We propose the continuous-variable quantum key distribution protocol based on the Gaussian modulation of a single quadrature of the coherent states of light, which is aimed to provide simplified implementation compared to the symmetrically modulated Gaussian coherent-state protocols. The protocol waives the necessity in one of the quadrature modulations and the corresponding channel transmittance estimation. The security of the protocol against collective attacks in a generally phase-sensitive Gaussian channel is analyzed and is shown achievable upon certain conditions. Robustness of the protocol to channel imperfections is compared to that of the symmetrical coherent-state protocol. The simplified unidimensional protocol is shown possible at a reasonable quantitative cost in terms of key rate and of tolerable channel excess noise.
We propose a novel heterodyne detection scheme for continuous-variable quantum key distribution (CVQKD), which measures both quadrature components of a quantum signal encoded in optical phase space. The proposed method uses time division to achieve identical performance to conventional heterodyne detection with only a single homodyne detection system. Our method also uses a Faraday-Michelson interferometer to make it independent of polarization drift and eliminate the need for dynamic polarization control. Our method is experimentally demonstrated using the Gaussian-modulated coherent-states (GMCS) protocol over a 20.06 km optical fiber channel, achieving an expected secret key rate of up to 0.187 Mbps.
We propose a novel heterodyne detection scheme for continuous-variable quantum key distribution (CVQKD), which measures both quadrature components of a quantum signal encoded in optical phase space. The proposed method uses time division to achieve identical performance to conventional heterodyne detection with only a single homodyne detection system. Our method also uses a Faraday-Michelson interferometer to make it independent of polarization drift and eliminate the need for dynamic polarization control. Our method is experimentally demonstrated using the Gaussian-modulated coherent-states (GMCS) protocol over a 20.06 km optical fiber channel, achieving an expected secret key rate of up to 0.187 Mbps.