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Applied Physics Letters

Generation of −10.7 dB unbiased entangled states of light

Yajun Wang, Wenhui Zhang, Ruixin Li, Long Tian, Yaohui Zheng

Published Mar 29, 2021• 20 citations
Publisher

Abstract

In a continuous variable quantum key distribution (CV-QKD) system, strong Einstein–Podolsky–Rosen entangled states can significantly boost the robustness and distance for secure communication. However, an inevitable bias of two entanglement quadratures may degrade the secret key rate and distance during random quadrature base switching. The bias originates from several interdependent factors in the generation, propagation, and detection of entangled states, which faces a challenge to be completely eliminated. Here, we analyze in detail the origin of the bias effect and report on a scheme of generating unbiased entangled states, whereby a −10.7 ± 0.1 dB quadrature noise unbiased entanglement is first generated experimentally with two single-mode squeezed states. The unbiased quadrature correlations within the measurement bandwidth are expected to immensely enhance the key rate and secure distance for CV-QKD.

DOI
10.1063/5.0041289

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In a continuous variable quantum key distribution (CV-QKD) system, strong Einstein–Podolsky–Rosen entangled states can significantly boost the robustness and distance for secure communication. However, an inevitable bias of two entanglement quadratures may degrade the secret key rate and distance during random quadrature base switching. The bias originates from several interdependent factors in the generation, propagation, and detection of entangled states, which faces a challenge to be completely eliminated. Here, we analyze in detail the origin of the bias effect and report on a scheme of generating unbiased entangled states, whereby a −10.7 ± 0.1 dB quadrature noise unbiased entanglement is first generated experimentally with two single-mode squeezed states. The unbiased quadrature correlations within the measurement bandwidth are expected to immensely enhance the key rate and secure distance for CV-QKD.
Einstein-Podolsky-Rosen (EPR) entangled states can significantly enhance the secret key rate and secure distance of continuous-variable quantum key distribution (CV-QKD). In practical imperfections always exist in the preparation of two-mode squeezing (entangled states), which present an asymmetrical variance for the two quadratures. The imperfections induced by the bias effect of the entangled states are commonly treated as part of the untrusted channel to decrease the performance of the system. Here, we theoretically quantify the influence of bias effect on the secret key rate and secure distance, and propose a solution of generating unbiased entangled states protocol. The results demonstrated that the unbiased entangled states protocol guarantees the longest secure distance and highest key rate compared to that of coherent and biased entangled states.
Secure communication protocols based on quantum physics compel worldwide attention. Continuous-variable quantum key distribution (CV-QKD) uses a cost-effective detection technique instead of dedicated single-photon-counting technology, and can provide high key rates over metropolitan distances. Traditional coherent-state CV-QKD protocols, however, suffer from low tolerance of channel excess noise. The authors succeed in distributing Einstein-Podolsky-Rosen entangled states over a 50-km standard fiber with negligible excess noise, and further demonstrate CV-QKD in a high-noise environment with performance superior to that of the optimized coherent-state protocol.
Continuous-variable quantum key distribution (CV-QKD), which uses quadratures of the electromagnetic field, enables practical quantum communication using standard telecommunication technologies. Unidimensional CV-QKD (UD-CVQKD) simplifies the implementation by restricting modulation to a single quadrature. In this work, we experimentally demonstrate a free-space Gaussian-modulated UD-CVQKD system operating under a high detector electronic-noise regime (1.4 shot-noise units). The system employs polarized coherent states with signal and local oscillator co-propagating in the same spatial mode in orthogonal polarizations, ensuring stable interference. System security is analyzed under both untrusted (UTD) and trusted (TD) detector noise models. While no positive secret key rate is obtained under the UTD model, the TD model enables secure key generation over a finite range of modulation variances, highlighting the critical role of detector trust in high-noise conditions. A maximum secret key rate of 270 kbps is achieved at an optimal modulation variance of 11.57. Furthermore, secure operation requires high-transmittance (low-loss) channels under such noise conditions. This study demonstrates the practical feasibility of free-space UD-CVQKD in realistic high electronic-noise detection constraints and highlights detector electronic noise as a key limiting factor in practical systems.
Einstein-Podolsky-Rosen (EPR) entanglement is a criterion that is more demanding than just certifying entanglement. We theoretically and experimentally analyze the low-resource generation of bipartite continuous-variable entanglement, as realized by mixing a squeezed mode with a vacuum mode at a balanced beam splitter, i.e., the generation of so-called vacuum-class entanglement. We find that in order to observe EPR entanglement the total optical loss must be smaller than 33.333.333.3 %. However, arbitrarily strong EPR entanglement is generally possible with this scheme. We realize continuous-wave squeezed light at 155015501550 nm with up to 9.99.99.9 dB of nonclassical noise reduction, which is the highest value at a telecom wavelength so far. Using two phase-controlled balanced homodyne detectors we observe an EPR covariance product of $0.502\ifmmode\pm\else\textpm\fi{}0.006<1$, where 111 is the critical value. We discuss the feasibility of strong Gaussian entanglement and its application for quantum key distribution in a short-distance fiber network.
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.
We report on the development of continuous-variable quantum key distribution (CV-QKD) system that are based on discrete quadrature amplitude modulation (QAM) and homodyne detection of coherent states of light. We use a pulsed light source whose wavelength is 1550 nm and repetition rate is 10 MHz. The CV-QKD system can continuously generate secret key which is secure against entangling cloner attack. Key generation rate is 50 kbps when the quantum channel is a 10 km optical fiber. The CV-QKD system we have developed utilizes the four-state and post-selection protocol [T. Hirano, et al., Phys. Rev. A 68, 042331 (2003).]; Alice randomly sends one of four states {|±α⟩,|±𝑖α⟩}, and Bob randomly performs x- or p- measurement by homodyne detection. A commercially available balanced receiver is used to realize shot-noise-limited pulsed homodyne detection. GPU cards are used to accelerate the software-based post-processing. We use a non-binary LDPC code for error correction (reverse reconciliation) and the Toeplitz matrix multiplication for privacy amplification.