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Journal of Bioengineering, Technologies and Health

Analysis of the Impact of Homodyne Detection Efficiency on Remote State Preparation

Wagner C. Normando Filho, L. J. Pereira, Alexandre B. Tacla

Published Apr 28, 2026• 0 citations
Publisher

Abstract

Continuous-variable quantum key distribution (CV-QKD) is a leading technology for secure communication, whose security guarantees fundamentally rely on the quantum nature of the transmitted states and the measurement process. However, real-world detectors invariably suffer from limitations, such as inefficiency, which affects the overall security and performance of the system. Here, we investigate the impact of detector efficiency on remote state preparation in the context of entanglement-based CV-QKD. Specifically, by using the Wigner function formalism and starting from a two-mode squeezed vacuum state, we derive the analyticalform of the quantum state of one mode conditioned on a homodyne measurement performed on the other mode. Our analysis explicitly contrasts the ideal case of unit efficiency (η=1), which prepares a pure, displaced squeezed state, with the non-ideal scenario. For η < 1, we demonstrate that the preparation result is a mixedstate characterized by increased noise and degraded squeezing. We calculate the exact analytical expressions for the conditional state’s variance and mean displacement, quantifying their dependence on both the efficiency η and the initial squeezing parameter.

DOI
10.34178/jbth.v9i3.600

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Continuous-variable quantum key distribution (CV-QKD) is a leading technology for secure communication, whose security guarantees fundamentally rely on the quantum nature of the transmitted states and the measurement process. However, real-world detectors invariably suffer from limitations, such as inefficiency, which affects the overall security and performance of the system. Here, we investigate the impact of detector efficiency on remote state preparation in the context of entanglement-based CV-QKD. Specifically, by using the Wigner function formalism and starting from a two-mode squeezed vacuum state, we derive the analyticalform of the quantum state of one mode conditioned on a homodyne measurement performed on the other mode. Our analysis explicitly contrasts the ideal case of unit efficiency (η=1), which prepares a pure, displaced squeezed state, with the non-ideal scenario. For η < 1, we demonstrate that the preparation result is a mixedstate characterized by increased noise and degraded squeezing. We calculate the exact analytical expressions for the conditional state’s variance and mean displacement, quantifying their dependence on both the efficiency η and the initial squeezing parameter.
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Continuous variable-quantum key distribution (CV-QKD) based on coherent detection has potential to be a cost-effective solution to deploy secure keys over optical networks. This is due to its compatibility with mature optical communication technologies, such as homodyne and heterodyne detection schemes. Nevertheless, realistic implementations of CV-QKD systems suffer from imperfections in the practical devices used to generate and detect the coherent states. Those imperfections deteriorate the performance of the CV-QKD system and can be exploited by an eavesdropper to steal key information without being detected. In this work, we discuss the impact of practical device imperfections on the excess noise of the CV-QKD and on the achievable transmission distance. We also analyze the impact of detection imperfections on the measurement of the shot noise, and its impact on CV-QKD system security.
We propose a rigorous calibration method for homodyne detection efficiency, which combines all the factors that affect detection efficiency to calibrate together through the actual homodyne detection. With this method, the transmittance converted from electronic noise in the one-time calibration method of the shot noise can be attributed to the detection inefficiency. Thus, a trusted detection noise-free model for continuous-variable quantum key distribution (CV-QKD) can be established, which simplifies the calibration of shot noise while having the same performance as the trusted detection noise model. We demonstrate this calibration method with a balanced detector based on a transimpedance amplifier. Experimental results show that detection efficiency will be overestimated if the integration factor of the detector is overlooked. The overestimation of the detection efficiency leads to an underestimation of modulation variance and excess noise when the modulation variance is monitored by the balanced detector, which opens security loopholes. Our method may prove a necessary method in the calibration of detection efficiency for CV-QKD.
Continuous-variable quantum key distribution (CV-QKD) has emerged as a leading protocol for provably secure cryptographic key exchange, leveraging quantum properties of optical signals while remaining compatible with existing telecom infrastructure.In these systems, the receiver's detection capability directly impacts the rate at which cryptographic keys can be generated, making it a critical factor for real-time secure communications.Conventional coherent reception schemes (based solely on Gaussian operations) are fundamentally limited in their ability to distinguish quantum states, performing below the ultimate limit allowed by quantum mechanics.Overcoming this limitation requires non-Gaussian detection strategies, which can approach this theoretical bound and unlock higher key generation rates.In this work, we investigate the optimized displacement receiver (ODR) -a non-Gaussian strategy that combines a signal preprocessing step with photon countingas an alternative to conventional homodyne detection for CV-QKD protocols employing binary phase-shift keying (BPSK) modulation.We evaluate its security performance under realistic conditions by modeling practical detector imperfections such as efficiency loss and noise.Our results show that the ODR achieves higher secret key rates than conventional homodyne detection for all detector efficiencies, at all distances, and across the range of detector noise relevant for practical devices, directly translating into enhanced cryptographic performance and extended transmission range.
Continuous-variable quantum key distribution (CV-QKD) enables two remote parties to establish information-theoretically secure keys and offers high practical feasibility due to its compatibility with mature coherent optical communication technologies. However, as CV-QKD systems progress toward digital implementations, device nonidealities drive the optical field from a single-mode to a continuous-mode region, thereby underscoring the mismatch between theoretical models and practical systems. Here, we introduce temporal modes to construct an entanglement-based scheme that more accurately captures device nonidealities and develop a corresponding secret key rate calculation method applicable to continuous-mode scenarios. We demonstrate that optimizing the pulse-shaping format can significantly improve performance under detector-bandwidth-limited conditions. Experimental results also confirm that the proposed model effectively describes the impact of sampling-time deviations. We further analyze a linear weighted-reconstruction digital signal processing method,which improves the secret key rate by approximately 50% in a 30-km fiber experiment without requiring additional hardware, demonstrating a substantial performance enhancement at metropolitan distances. The proposed theoretical framework accommodates a broader range of experimental conditions and can guide the optimization of digital CV-QKD systems.
In continuous-variable quantum key distribution (CV-QKD), the key information are encoded on quadratures of the optical field, which are measured via balanced homodyne detector (BHD). The bandwidth of the BHD is one of key parameters for precise characterization of quantum states. We establish a theoretical model to analyze the impact of the BHD bandwidth and signal modulation patterns on the channel parameters estimation of CV-QKD systems. Based on the proposed model, the secure key rate of a practical CV-QKD system under different BHD bandwidths and signal modulation patterns are investigated. Our results show that insufficient BHD bandwidth will result in wrong estimate of the transmission loss and excess noise, which significantly affects the performance of CV-QKD systems. Given the BHD bandwidth, there exists an optimal signal repetition rate that maximizes the secure key rate. The BHD bandwidth requirement of the QKD system increases with the transmission distance for large duty cycle pulse. Furthermore, the root raised-cosine pulse signal modulation performs better than the square pulse signal modulation in general.