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:1302.5087 · Physical Review A

Missing data outside the detector range: Continuous-variable entanglement verification and quantum cryptography

Megan R. Ray, S. J. van Enk

Published Oct 18, 2013• 12 citations
arXivHTMLPDF

Abstract

In continuous-variable quantum information processing, detectors are necessarily coarse grained and of finite range. We discuss how, especially, the latter feature is a bug and may easily lead to overoptimistic estimates of entanglement and of security when missed data outside the detector range are ignored. We demonstrate that a straightforward worst-case analysis is sufficient to avoid false positive statements about entanglement. We show that, for our worst-case analysis, entropic separability or security criteria are much superior to variance-based criteria.

DOI
10.1103/physreva.88.042326

Related papers

Missing data outside the detector range. II. Application to time-frequency entanglement

Megan R. Ray, S. J. van Enk

In a previous paper, we pointed out the problem of missing data outside the detector range for continuous-variable entanglement verification and quantum key distribution, and we provided a straightforward solution based on entropic separability criteria (as those work better than variance-based criteria). We apply that solution here to the verification of time-frequency entanglement of photon pairs, particularly to the quantum key distribution scheme proposed by Nunn et al. [Opt. Express 21, 15959 (2013)]. We find that the scheme does lead to verifiable entanglement, but that transmission noise quickly destroys the ability to verify the entanglement.

Physical Review A•Dec 20, 2013•6 citations

Impact of coarse-grained measurement with finite range on continuous-variable quantum key distribution

Tianyi Wang, Song Yu, Wanyi Gu

In continuous-variable quantum key distribution, detectors are necessarily coarse grained and of finite range. We analyze the impact of both features and demonstrate that while coarse graining adds a fixed error to the estimated excess noise, finite range degrades the estimation accuracy of both transmission and excess noise. Moreover, the inaccurate estimation due to finite range may results in secret key rate underestimation, even misjudgment of security. To compensate these consequences, tuning the modulation variance is a possible way.

Journal of Modern Optics•Oct 22, 2015•1 citation

Uncertainty Relations for Coarse-Grained Measurements: An Overview

Toscano, F., Tasca, D., Rudnicki, Ł. +1 more

Uncertainty relations involving incompatible observables are one of the cornerstones of quantum mechanics. Aside from their fundamental significance, they play an important role in practical applications, such as detection of quantum correlations and security requirements in quantum cryptography. In continuous variable systems, the spectra of the relevant observables form a continuum and this necessitates the coarse graining of measurements. However, these coarse-grained observables do not necessarily obey the same uncertainty relations as the original ones, a fact that can lead to false results when considering applications. That is, one cannot naively replace the original observables in the uncertainty relation for the coarse-grained observables and expect consistent results. As such, several uncertainty relations that are specifically designed for coarse-grained observables have been developed. In recognition of the 90th anniversary of the seminal Heisenberg uncertainty relation, celebrated last year, and all the subsequent work since then, here we give a review of the state of the art of coarse-grained uncertainty relations in continuous variable quantum systems, as well as their applications to fundamental quantum physics and quantum information tasks. Our review is meant to be balanced in its content, since both theoretical considerations and experimental perspectives are put on an equal footing.

•Jun 1, 2018•16 citations

Uncertainty Relations for Coarse–Grained Measurements: An Overview

Fabricio Toscano, Daniel S. Tasca, Łukasz Rudnicki +1 more

Uncertainty relations involving incompatible observables are one of the cornerstones of quantum mechanics. Aside from their fundamental significance, they play an important role in practical applications, such as detection of quantum correlations and security requirements in quantum cryptography. In continuous variable systems, the spectra of the relevant observables form a continuum and this necessitates the coarse graining of measurements. However, these coarse-grained observables do not necessarily obey the same uncertainty relations as the original ones, a fact that can lead to false results when considering applications. That is, one cannot naively replace the original observables in the uncertainty relation for the coarse-grained observables and expect consistent results. As such, several uncertainty relations that are specifically designed for coarse-grained observables have been developed. In recognition of the 90th anniversary of the seminal Heisenberg uncertainty relation, celebrated last year, and all the subsequent work since then, here we give a review of the state of the art of coarse-grained uncertainty relations in continuous variable quantum systems, as well as their applications to fundamental quantum physics and quantum information tasks. Our review is meant to be balanced in its content, since both theoretical considerations and experimental perspectives are put on an equal footing.

arXiv:1805.00782•Entropy•Jun 10, 2018•22 citations

Entropic uncertainty relations and the measurement range problem, with consequences for high-dimensional quantum key distribution

J. Eli Bourassa, Hoi‐Kwong Lo

The measurement range problem, where one cannot determine the data outside the range of the detector, limits the characterization of entanglement in high-dimensional quantum systems when employing, among other tools from information theory, the entropic uncertainty relations. Practically, the measurement range problem weakens the security of entanglement-based large-alphabet quantum key distribution (QKD) employing degrees of freedom including time-frequency or electric field quadrature. We present a modified entropic uncertainty relation that circumvents the measurement range problem under certain conditions and apply it to well-known QKD protocols. For time-frequency QKD, although our bound is an improvement, we find that high channel loss poses a problem for its feasibility. In homodyne-based continuous variable QKD, we find our bound provides a quantitative way to monitor for saturation attacks.

arXiv:1810.05654•Journal of the Optical Society of America B•Jan 31, 2019•7 citations

Reliable Entanglement Detection under Coarse-Grained Measurements

D. S. Tasca, Łukasz Rudnicki, Rafael M. Gomes +2 more

We derive reliable entanglement witnesses for coarse-grained measurements on continuous variable systems. These witnesses never return a "false positive" for identification of entanglement, under any degree of coarse graining. We show that even in the case of Gaussian states, entanglement witnesses based on the Shannon entropy can outperform those based on variances. We apply our results to experimental identification of spatial entanglement of photon pairs.

arXiv:1210.5945•Physical Review Letters•May 1, 2013•44 citations
In continuous-variable quantum information processing, detectors are necessarily coarse grained and of finite range. We discuss how, especially, the latter feature is a bug and may easily lead to overoptimistic estimates of entanglement and of security when missed data outside the detector range are ignored. We demonstrate that a straightforward worst-case analysis is sufficient to avoid false positive statements about entanglement. We show that, for our worst-case analysis, entropic separability or security criteria are much superior to variance-based criteria.
In a previous paper, we pointed out the problem of missing data outside the detector range for continuous-variable entanglement verification and quantum key distribution, and we provided a straightforward solution based on entropic separability criteria (as those work better than variance-based criteria). We apply that solution here to the verification of time-frequency entanglement of photon pairs, particularly to the quantum key distribution scheme proposed by Nunn et al. [Opt. Express 21, 15959 (2013)]. We find that the scheme does lead to verifiable entanglement, but that transmission noise quickly destroys the ability to verify the entanglement.
In continuous-variable quantum key distribution, detectors are necessarily coarse grained and of finite range. We analyze the impact of both features and demonstrate that while coarse graining adds a fixed error to the estimated excess noise, finite range degrades the estimation accuracy of both transmission and excess noise. Moreover, the inaccurate estimation due to finite range may results in secret key rate underestimation, even misjudgment of security. To compensate these consequences, tuning the modulation variance is a possible way.
Uncertainty relations involving incompatible observables are one of the cornerstones of quantum mechanics. Aside from their fundamental significance, they play an important role in practical applications, such as detection of quantum correlations and security requirements in quantum cryptography. In continuous variable systems, the spectra of the relevant observables form a continuum and this necessitates the coarse graining of measurements. However, these coarse-grained observables do not necessarily obey the same uncertainty relations as the original ones, a fact that can lead to false results when considering applications. That is, one cannot naively replace the original observables in the uncertainty relation for the coarse-grained observables and expect consistent results. As such, several uncertainty relations that are specifically designed for coarse-grained observables have been developed. In recognition of the 90th anniversary of the seminal Heisenberg uncertainty relation, celebrated last year, and all the subsequent work since then, here we give a review of the state of the art of coarse-grained uncertainty relations in continuous variable quantum systems, as well as their applications to fundamental quantum physics and quantum information tasks. Our review is meant to be balanced in its content, since both theoretical considerations and experimental perspectives are put on an equal footing.
Uncertainty relations involving incompatible observables are one of the cornerstones of quantum mechanics. Aside from their fundamental significance, they play an important role in practical applications, such as detection of quantum correlations and security requirements in quantum cryptography. In continuous variable systems, the spectra of the relevant observables form a continuum and this necessitates the coarse graining of measurements. However, these coarse-grained observables do not necessarily obey the same uncertainty relations as the original ones, a fact that can lead to false results when considering applications. That is, one cannot naively replace the original observables in the uncertainty relation for the coarse-grained observables and expect consistent results. As such, several uncertainty relations that are specifically designed for coarse-grained observables have been developed. In recognition of the 90th anniversary of the seminal Heisenberg uncertainty relation, celebrated last year, and all the subsequent work since then, here we give a review of the state of the art of coarse-grained uncertainty relations in continuous variable quantum systems, as well as their applications to fundamental quantum physics and quantum information tasks. Our review is meant to be balanced in its content, since both theoretical considerations and experimental perspectives are put on an equal footing.
The measurement range problem, where one cannot determine the data outside the range of the detector, limits the characterization of entanglement in high-dimensional quantum systems when employing, among other tools from information theory, the entropic uncertainty relations. Practically, the measurement range problem weakens the security of entanglement-based large-alphabet quantum key distribution (QKD) employing degrees of freedom including time-frequency or electric field quadrature. We present a modified entropic uncertainty relation that circumvents the measurement range problem under certain conditions and apply it to well-known QKD protocols. For time-frequency QKD, although our bound is an improvement, we find that high channel loss poses a problem for its feasibility. In homodyne-based continuous variable QKD, we find our bound provides a quantitative way to monitor for saturation attacks.