Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2205.10142 · Physical Review A

Data postprocessing for the one-way heterodyne protocol under composable finite-size security

Alexander G. Mountogiannakis, Panagiotis Papanastasiou, Stefano Pirandola

Published Oct 6, 2022• 17 citations
arXivHTMLPDF

Abstract

The performance of a practical continuous-variable quantum key distribution protocol depends significantly, apart from the loss and noise of the quantum channel, on the postprocessing steps which lead to the extraction of the final secret key. A critical step is the reconciliation process, especially when one assumes finite-size effects in a composable framework. Here, we focus on the Gaussian-modulated coherent-state protocol with heterodyne detection in a high signal-to-noise ratio regime. We simulate the quantum communication process and we postprocess the output data by applying parameter estimation, error correction (using high-rate, nonbinary low-density parity-check codes) and privacy amplification. This allows us to study the performance for practical implementations of the protocol and optimize the parameters connected to the steps above. We also present an associated Python library performing the steps above.

DOI
10.1103/physreva.106.042606

Related papers

Composably secure data processing for Gaussian-modulated continuous-variable quantum key distribution

Alexander G. Mountogiannakis, Panagiotis Papanastasiou, Boris Braverman +1 more

Continuous-variable (CV) quantum key distribution (QKD) employs the quadratures of a bosonic mode to establish a secret key between two remote parties, and this is usually achieved via a Gaussian modulation of coherent states. The resulting secret key rate depends not only on the loss and noise in the communication channel, but also on a series of data processing steps that are needed for transforming shared correlations into a final string of secret bits. Here we consider a Gaussian-modulated coherent-state protocol with homodyne detection in the general setting of composable finite-size security. After simulating the process of quantum communication, the output classical data are postprocessed via procedures of parameter estimation, error correction, and privacy amplification. In particular, we analyze the high signal-to-noise regime, which requires the use of high-rate (nonbinary) low-density parity check codes. We implement all these steps in a python-based library that allows one to investigate and optimize the protocol parameters to be used in practical experimental implementations of short-range CV-QKD.

arXiv:2103.16589•Physical Review Research•Feb 9, 2022•30 citations

Composable finite-size effects in free-space continuous-variable quantum-key-distribution systems

Nedasadat Hosseinidehaj, Nathan Walk, Timothy C. Ralph

Free-space channels provide the possibility of establishing continuous-variable quantum key distribution in global communication networks. However, the fluctuating nature of transmissivity in these channels introduces an extra noise which reduces the achievable secret key rate. We consider two classical postprocessing strategies, postselection of high-transmissivity data and data clusterization, to reduce the fluctuation-induced noise of the channel. We undertake the investigation of such strategies utilizing a composable security proof in a realistic finite-size regime against both collective and individual attacks. We also present an efficient parameter estimation approach to estimate the effective Gaussian parameters over the postselected data or the clustered data. Although the composable finite-size effects become more significant with the postselection and clusterization both reducing the size of the data, our results show that these strategies are still able to enhance the finite-size key rate against both individual and collective attacks with a remarkable improvement against collective attacks, even moving the protocol from an insecure regime to a secure regime under certain conditions.

arXiv:2002.03476•Physical Review A•Jan 20, 2021•40 citations

Spherical reconciliation for a continuous-variable quantum key distribution

Lu Zhao, Jianhong Shi, Feng‐Guang Li

Information reconciliation is a significant step for a continuous-variable quantum key distribution (CV-QKD) system. We propose a reconciliation method that allows two authorized parties to extract a consistent and secure binary key in a CV-QKD protocol, which is based on Gaussian-modulated coherent states and homodyne detection. This method named spherical reconciliation is based on spherical quantization and non-binary low-density parity-check (LDPC) codes. With the suitable signal-to-noise ratio (SNR) and code rate of non-binary LDPC codes, spherical reconciliation algorithm has a high efficiency and can extend the transmission distance of CV-QKD.

Chinese Physics B•Apr 1, 2017•3 citations

Secret key extraction in direct reconciliation CV-QKD systems

Margarida Almeida, M. Facão, Nelson Jesus Muga +2 more

Quantum Key Distribution (QKD) is, nowadays, the dominant practical application in the quantum technologies field. Nevertheless, extracting secure keys from a physical implementation of a QKD system remains a complicated procedure. In this paper, post-processing algorithms were implemented to extract secret keys from a Continuous-Variable QKD (CV-QKD) system. The Discrete Modulated Four State CV-QKD protocol was considered due to lower complexity in the reconciliation procedure. The secret keys were extracted considering Maximum-Likelihood Estimators (MLEs) for parameter estimation, Iterative Low-Density Parity Check (LDPC) codes complemented with the Sum-Product Algorithm and error groups iterative reconciliation for information reconciliation, and the Toeplitz matrix as the universal hash function for privacy amplification. The post-processing algorithms were applied to extract secret keys from a simulated implementation of the Discrete Modulated Four State CV-QKD protocol, with double homodyne detection.

Telecoms Conference (ConfTELE)•Feb 11, 2021•2 citations

Long-distance continuous-variable quantum key distribution with a Gaussian modulation

Paul Jouguet, Sébastien Kunz-Jacques, Anthony Leverrier

We designed high-efficiency error correcting codes allowing us to extract an errorless secret key in a continuous-variable quantum key distribution (CVQKD) protocol using a Gaussian modulation of coherent states and a homodyne detection. These codes are available for a wide range of signal-to-noise ratios on an additive white Gaussian noise channel with a binary modulation and can be combined with a multidimensional reconciliation method proven secure against arbitrary collective attacks. This improved reconciliation procedure considerably extends the secure range of a CVQKD with a Gaussian modulation, giving a secret key rate of about ${10}^{\ensuremath{-}3}$ bit per pulse at a distance of 120 km for reasonable physical parameters.

arXiv:1110.0100•Physical Review A•Dec 21, 2011•273 citations

Practical no-switching continuous-variable quantum key distribution with biased quadrature detection

Jiale Mi, Yiming Bian, Lu Fan +2 more

Continuous-variable quantum key distribution protocol using coherent states and heterodyne detection, called the no-switching protocol, is widely used in practical systems due to the simple experimental setup without basis switching and easy assessment to phase information. The security of an ideal no-switching protocol has been proved against general attacks in the finite-size regime and composable security framework, whose heterodyne detector consists of a beam splitter with transmittance of $50\mathrm{%}$ and two ideal homodyne detectors. However, the transmittance of a beam splitter is inaccurate and the two detectors always have different quantum efficiency and electronic noise, which introduce asymmetry into the heterodyne detection, and further lead to the mismatch between the ideal protocol and practical systems, thereby overestimating the secret key rate and resulting in a practical security loophole. In this paper, we close this loophole by proposing a modified no-switching protocol with biased quadrature detection, where the asymmetry of the heterodyne detection is modeled to match the practical systems, and the security of the protocol is analyzed in asymptotic and finite-size regimes. Further, an optimization strategy is proposed to achieve the optimal secret key rate by adjusting the transmittance of the beam splitter. Simulation results show the necessity of considering the asymmetry in heterodyne detection and the effectiveness of the optimization, which provides a promising way to realize a practical secure and high-performance no-switching system.

arXiv:2402.00277•Physical Review Applied•Jun 25, 2024•1 citation
The performance of a practical continuous-variable quantum key distribution protocol depends significantly, apart from the loss and noise of the quantum channel, on the postprocessing steps which lead to the extraction of the final secret key. A critical step is the reconciliation process, especially when one assumes finite-size effects in a composable framework. Here, we focus on the Gaussian-modulated coherent-state protocol with heterodyne detection in a high signal-to-noise ratio regime. We simulate the quantum communication process and we postprocess the output data by applying parameter estimation, error correction (using high-rate, nonbinary low-density parity-check codes) and privacy amplification. This allows us to study the performance for practical implementations of the protocol and optimize the parameters connected to the steps above. We also present an associated Python library performing the steps above.
Continuous-variable (CV) quantum key distribution (QKD) employs the quadratures of a bosonic mode to establish a secret key between two remote parties, and this is usually achieved via a Gaussian modulation of coherent states. The resulting secret key rate depends not only on the loss and noise in the communication channel, but also on a series of data processing steps that are needed for transforming shared correlations into a final string of secret bits. Here we consider a Gaussian-modulated coherent-state protocol with homodyne detection in the general setting of composable finite-size security. After simulating the process of quantum communication, the output classical data are postprocessed via procedures of parameter estimation, error correction, and privacy amplification. In particular, we analyze the high signal-to-noise regime, which requires the use of high-rate (nonbinary) low-density parity check codes. We implement all these steps in a python-based library that allows one to investigate and optimize the protocol parameters to be used in practical experimental implementations of short-range CV-QKD.
Free-space channels provide the possibility of establishing continuous-variable quantum key distribution in global communication networks. However, the fluctuating nature of transmissivity in these channels introduces an extra noise which reduces the achievable secret key rate. We consider two classical postprocessing strategies, postselection of high-transmissivity data and data clusterization, to reduce the fluctuation-induced noise of the channel. We undertake the investigation of such strategies utilizing a composable security proof in a realistic finite-size regime against both collective and individual attacks. We also present an efficient parameter estimation approach to estimate the effective Gaussian parameters over the postselected data or the clustered data. Although the composable finite-size effects become more significant with the postselection and clusterization both reducing the size of the data, our results show that these strategies are still able to enhance the finite-size key rate against both individual and collective attacks with a remarkable improvement against collective attacks, even moving the protocol from an insecure regime to a secure regime under certain conditions.
Information reconciliation is a significant step for a continuous-variable quantum key distribution (CV-QKD) system. We propose a reconciliation method that allows two authorized parties to extract a consistent and secure binary key in a CV-QKD protocol, which is based on Gaussian-modulated coherent states and homodyne detection. This method named spherical reconciliation is based on spherical quantization and non-binary low-density parity-check (LDPC) codes. With the suitable signal-to-noise ratio (SNR) and code rate of non-binary LDPC codes, spherical reconciliation algorithm has a high efficiency and can extend the transmission distance of CV-QKD.
Quantum Key Distribution (QKD) is, nowadays, the dominant practical application in the quantum technologies field. Nevertheless, extracting secure keys from a physical implementation of a QKD system remains a complicated procedure. In this paper, post-processing algorithms were implemented to extract secret keys from a Continuous-Variable QKD (CV-QKD) system. The Discrete Modulated Four State CV-QKD protocol was considered due to lower complexity in the reconciliation procedure. The secret keys were extracted considering Maximum-Likelihood Estimators (MLEs) for parameter estimation, Iterative Low-Density Parity Check (LDPC) codes complemented with the Sum-Product Algorithm and error groups iterative reconciliation for information reconciliation, and the Toeplitz matrix as the universal hash function for privacy amplification. The post-processing algorithms were applied to extract secret keys from a simulated implementation of the Discrete Modulated Four State CV-QKD protocol, with double homodyne detection.
We designed high-efficiency error correcting codes allowing us to extract an errorless secret key in a continuous-variable quantum key distribution (CVQKD) protocol using a Gaussian modulation of coherent states and a homodyne detection. These codes are available for a wide range of signal-to-noise ratios on an additive white Gaussian noise channel with a binary modulation and can be combined with a multidimensional reconciliation method proven secure against arbitrary collective attacks. This improved reconciliation procedure considerably extends the secure range of a CVQKD with a Gaussian modulation, giving a secret key rate of about ${10}^{\ensuremath{-}3}$ bit per pulse at a distance of 120 km for reasonable physical parameters.
Continuous-variable quantum key distribution protocol using coherent states and heterodyne detection, called the no-switching protocol, is widely used in practical systems due to the simple experimental setup without basis switching and easy assessment to phase information. The security of an ideal no-switching protocol has been proved against general attacks in the finite-size regime and composable security framework, whose heterodyne detector consists of a beam splitter with transmittance of $50\mathrm{%}$ and two ideal homodyne detectors. However, the transmittance of a beam splitter is inaccurate and the two detectors always have different quantum efficiency and electronic noise, which introduce asymmetry into the heterodyne detection, and further lead to the mismatch between the ideal protocol and practical systems, thereby overestimating the secret key rate and resulting in a practical security loophole. In this paper, we close this loophole by proposing a modified no-switching protocol with biased quadrature detection, where the asymmetry of the heterodyne detection is modeled to match the practical systems, and the security of the protocol is analyzed in asymptotic and finite-size regimes. Further, an optimization strategy is proposed to achieve the optimal secret key rate by adjusting the transmittance of the beam splitter. Simulation results show the necessity of considering the asymmetry in heterodyne detection and the effectiveness of the optimization, which provides a promising way to realize a practical secure and high-performance no-switching system.