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:1105.0628 · Physica A Statistical Mechanics and its Applications

Statistical measures of complexity for quantum systems with continuous variables

Daniel Manzano

Published Jul 2, 2012• 12 citations
arXivHTMLPDF
DOI
10.1016/j.physa.2012.06.058

Related papers

Gaussian quadrature inference for continuous-variable quantum key distribution

L. Gyongyosi, Sándor Imre

We propose the Gaussian quadrature inference (GQI) method for multicarrier continuous-variable quantum key distribution (CVQKD). A multicarrier CVQKD protocol utilizes Gaussian subcarrier quantum continuous variables (CV) for information transmission. The GQI framework provides a minimal error estimate of the quadratures of the CV quantum states from the discrete, measured noisy subcarrier variables. GQI utilizes the fundamentals of regularization theory and statistical information processing. We characterize GQI for multicarrier CVQKD, and define a method for the statistical modeling and processing of noisy Gaussian subcarrier quadratures. We demonstrate the results through the adaptive multicarrier quadrature division (AMQD) scheme. We introduce the terms statistical secret key rate and statistical private classical information, which quantities are derived purely by the statistical functions of GQI. We prove the secret key rate formulas for a multiple access multicarrier CVQKD via the AMQD-MQA (multiuser quadrature allocation) scheme. The framework can be established in an arbitrary CVQKD protocol and measurement setting, and are implementable by standard low-complexity statistical functions, which is particularly convenient for an experimental CVQKD scenario.

arXiv:1504.05574•Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 20, 2016•7 citations

On the statistical description of quantum systems

Stig Stenholm

Journal of Statistical Physics•Jan 1, 1971•3 citations

Statistical decision theory for quantum systems

Alexander Semenovich Holevo

Journal of Multivariate Analysis•Dec 1, 1973•645 citations

Statistical Quadrature Evolution by Inference for Continuous-Variable Quantum Key Distribution

László Gyöngyösi

We define the statistical quadrature evolution (QE) method for multicarrier continuous-variable quantum key distribution (CVQKD). A multicarrier CVQKD protocol uses Gaussian subcarrier quantum continuous variables (CVs) for information transmission. The QE scheme utilizes the theory of mathematical statistics and statistical information processing. The QE model is based on the Gaussian quadrature inference (GQI) framework to provide a minimal error estimate of the CV state quadratures. The QE block evaluates a unique and stable estimation of the non-observable continuous input from the measurement results and through the statistical inference method yielded from the GQI framework. The QE method minimizes the overall expected error by an estimator function and provides a viable, easily implementable, and computationally efficient way to maximize the extractable information from the observed data. The QE framework can be established in an arbitrary CVQKD protocol and measurement setting and is implementable by standard low-complexity functions, which is particularly convenient for experimental CVQKD.

arXiv:1603.09247•Mar 30, 2016•1 citation

Continuous-Variable Quantum State Tomography Enabled by Quantum Mirrors

Mariano Uria, Amaru Moya, Carla Hermann-Avigliano +2 more

In quantum technologies, continuous-variable systems offer advantages over their discrete counterparts. However, continuous-variable tomography suffers from exponentially growing sample complexity. We propose protocols using quantum mirrors to transfer the complete information of incident photonic states onto a control atomic system. This enables full photonic state characterization through measurements on the control atom alone, realized via kernel functions, direct wavefunction reconstruction, and pointwise Wigner function measurements. Our approach overcomes the limitations of conventional photon counting, statistical inference, and inverse transformation, providing a robust framework for benchmarking and verifying non-Gaussian states in continuous-variable quantum optics.

quant-pharXiv:2606.04277•Jun 4, 2026•0 citations

Cross-Platform Verification of Continuous-Variable Quantum Systems

Kun Wang

Cross-platform verification compares output states of independently operated bosonic and quantum optical systems when classical predictions and joint measurements are unavailable. Continuous-variable distributed inner product estimation (CV-DIPE) provides a local measurement approach, but infinite-dimensional state spaces require rigorous control of truncation error. We develop three CV-DIPE protocols for the natural class of energy-constrained continuous-variable quantum states. One uses coordinated displaced parity, another coordinated Haar measurements, and the third independent homodyne shadows. For arbitrary multimode inputs in this class, including entangled and non-Gaussian states, we establish truncation error bounds and worst-case sample complexity guarantees for the exact inner product. The leading terms of these bounds favor coordinated Haar measurements, whose global implementation is experimentally challenging. These protocols provide certified strategies for cross-platform verification of continuous-variable systems using only local measurement data.

quant-pharXiv:2610.39912•Oct 30, 2026•0 citations
We propose the Gaussian quadrature inference (GQI) method for multicarrier continuous-variable quantum key distribution (CVQKD). A multicarrier CVQKD protocol utilizes Gaussian subcarrier quantum continuous variables (CV) for information transmission. The GQI framework provides a minimal error estimate of the quadratures of the CV quantum states from the discrete, measured noisy subcarrier variables. GQI utilizes the fundamentals of regularization theory and statistical information processing. We characterize GQI for multicarrier CVQKD, and define a method for the statistical modeling and processing of noisy Gaussian subcarrier quadratures. We demonstrate the results through the adaptive multicarrier quadrature division (AMQD) scheme. We introduce the terms statistical secret key rate and statistical private classical information, which quantities are derived purely by the statistical functions of GQI. We prove the secret key rate formulas for a multiple access multicarrier CVQKD via the AMQD-MQA (multiuser quadrature allocation) scheme. The framework can be established in an arbitrary CVQKD protocol and measurement setting, and are implementable by standard low-complexity statistical functions, which is particularly convenient for an experimental CVQKD scenario.
We define the statistical quadrature evolution (QE) method for multicarrier continuous-variable quantum key distribution (CVQKD). A multicarrier CVQKD protocol uses Gaussian subcarrier quantum continuous variables (CVs) for information transmission. The QE scheme utilizes the theory of mathematical statistics and statistical information processing. The QE model is based on the Gaussian quadrature inference (GQI) framework to provide a minimal error estimate of the CV state quadratures. The QE block evaluates a unique and stable estimation of the non-observable continuous input from the measurement results and through the statistical inference method yielded from the GQI framework. The QE method minimizes the overall expected error by an estimator function and provides a viable, easily implementable, and computationally efficient way to maximize the extractable information from the observed data. The QE framework can be established in an arbitrary CVQKD protocol and measurement setting and is implementable by standard low-complexity functions, which is particularly convenient for experimental CVQKD.
In quantum technologies, continuous-variable systems offer advantages over their discrete counterparts. However, continuous-variable tomography suffers from exponentially growing sample complexity. We propose protocols using quantum mirrors to transfer the complete information of incident photonic states onto a control atomic system. This enables full photonic state characterization through measurements on the control atom alone, realized via kernel functions, direct wavefunction reconstruction, and pointwise Wigner function measurements. Our approach overcomes the limitations of conventional photon counting, statistical inference, and inverse transformation, providing a robust framework for benchmarking and verifying non-Gaussian states in continuous-variable quantum optics.
Cross-platform verification compares output states of independently operated bosonic and quantum optical systems when classical predictions and joint measurements are unavailable. Continuous-variable distributed inner product estimation (CV-DIPE) provides a local measurement approach, but infinite-dimensional state spaces require rigorous control of truncation error. We develop three CV-DIPE protocols for the natural class of energy-constrained continuous-variable quantum states. One uses coordinated displaced parity, another coordinated Haar measurements, and the third independent homodyne shadows. For arbitrary multimode inputs in this class, including entangled and non-Gaussian states, we establish truncation error bounds and worst-case sample complexity guarantees for the exact inner product. The leading terms of these bounds favor coordinated Haar measurements, whose global implementation is experimentally challenging. These protocols provide certified strategies for cross-platform verification of continuous-variable systems using only local measurement data.