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:1312.2604

The Relationship Between Discrete and Continuous Entropy in EPR-Steering Inequalities

James Schneeloch

Published Dec 9, 2013• 3 citations
arXivHTMLPDF

Abstract

This document expands upon the relationship between discrete and continuous entropy given in (Phys. Rev. Lett. 110 130407), \Violating Continuous Variable Einstein-Podolsky-Rosen Steering with Discrete Measurements". We provide a detailed derivation for the inequality relating the continuous conditional entropy to its discrete approximation, and show how this connection works between discrete and continuous entropic quantities in general. In addition, we use this connection to show how to derive the continuous variable Einstein-Podolsky-Rosen steering inequality with discrete measurements as seen in (Phys. Rev. Lett. 110 130407), and make an additional comment which strengthens this result.

DOI
10.48550/arxiv.1312.2604

Related papers

Violation of Continuous-Variable Einstein-Podolsky-Rosen Steering with Discrete Measurements

James Schneeloch, P. Ben Dixon, Gregory A. Howland +2 more

In this Letter, we derive an entropic Einstein-Podolsky-Rosen (EPR) steering inequality for continuous-variable systems using only experimentally measured discrete probability distributions and details of the measurement apparatus. We use this inequality to witness EPR steering between the positions and momenta of photon pairs generated in spontaneous parametric down-conversion. We examine the asymmetry between parties in this inequality, and show that this asymmetry can be used to reduce the technical requirements of experimental setups intended to demonstrate the EPR paradox. Furthermore, we develop a more stringent steering inequality that is symmetric between parties, and use it to show that the down-converted photon pairs also exhibit symmetric EPR steering.

arXiv:1210.4234•Physical Review Letters•Mar 27, 2013•87 citations

Witnessing Continuous Variable Einstein-Podolsky-Rosen Steering with Discrete Measurements

James Schneeloch, P. Ben Dixon, Gregory A. Howland +2 more

We create a stronger EPR-steering inequality for continuous variables using entropic uncertainty and discrete measurements. We explore the asymmetry in this inequality and develop a new symmetric inequality. We also violate these inequalities in experiment.

Frontiers in Optics•Jan 1, 2013•0 citations

Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox

Eric G. Cavalcanti, S. J. Jones, Howard M. Wiseman +1 more

We formally link the concept of steering (a concept created by Schr\"odinger but only recently formalized by Wiseman, Jones, and Doherty [Phys. Rev. Lett. 98, 140402 (2007)]) and the criteria for demonstrations of Einstein-Podolsky-Rosen (EPR) paradox introduced by Reid [Phys. Rev. A 40, 913 (1989)]. We develop a general theory of experimental EPR-steering criteria, derive a number of criteria applicable to discrete as well as continuous-variable observables, and study their efficacy in detecting that form of nonlocality in some classes of quantum states. We show that previous versions of EPR-type criteria can be rederived within this formalism, thus unifying these efforts from a modern quantum-information perspective and clarifying their conceptual and formal origin. The theory follows in close analogy with criteria for other forms of quantum nonlocality (Bell nonlocality and entanglement), and because it is a hybrid of those two, it may lead to insights into the relationship between the different forms of nonlocality and the criteria that are able to detect them.

arXiv:0907.1109•Physical Review A•Sep 18, 2009•608 citations

Entropic EPR Steering Inequalities

Curtis J. Broadbent, James Schneeloch, Stephen Patrick Walborn +2 more

We derive entropic Einstein-Podolsky-Rosen (EPR) steering inequalities from entropic uncertainty relations. This allows us to formulate inequalities that test for EPR steering correlations which are symmetric between parties, or occur between multiple degrees of freedom.

Frontiers in Optics•Jan 1, 2013•0 citations

Demonstrating continuous variable Einstein–Podolsky–Rosen steering in spite of finite experimental capabilities using Fano steering bounds

James Schneeloch, Samuel H. Knarr, Gregory A. Howland +1 more

We show how one can demonstrate continuous-variable Einstein–Podolsky–Rosen (EPR) steering without needing to characterize entire measurement probability distributions. To do this, we develop a modified Fano inequality useful for discrete measurements of continuous variables and use it to bound the conditional uncertainties in continuous-variable entropic EPR-steering inequalities. With these bounds, we show how one can hedge against experimental limitations including a finite detector size, dead space between pixels, and any such factors that impose an incomplete sampling of the true measurement probability distribution. Furthermore, we use experimental data from the position and momentum statistics of entangled photon pairs in parametric downconversion to show that this method is sufficiently sensitive for practical use.

arXiv:1410.8853•Journal of the Optical Society of America B•Feb 20, 2015•3 citations

Einstein-Podolsky-Rosen steering inequalities from entropic uncertainty relations

James Schneeloch, Curtis J. Broadbent, Stephen Patrick Walborn +2 more

We use entropic uncertainty relations to formulate inequalities that witness Einstein-Podolsky-Rosen (EPR)-steering correlations in diverse quantum systems. We then use these inequalities to formulate symmetric EPR-steering inequalities using the mutual information. We explore the differing natures of the correlations captured by one-way and symmetric steering inequalities and examine the possibility of exclusive one-way steerability in two-qubit states. Furthermore, we show that steering inequalities can be extended to generalized positive operator-valued measures, and we also derive hybrid steering inequalities between alternate degrees of freedom.

arXiv:1303.7432•Physical Review A•Jun 6, 2013•315 citations
This document expands upon the relationship between discrete and continuous entropy given in (Phys. Rev. Lett. 110 130407), \Violating Continuous Variable Einstein-Podolsky-Rosen Steering with Discrete Measurements". We provide a detailed derivation for the inequality relating the continuous conditional entropy to its discrete approximation, and show how this connection works between discrete and continuous entropic quantities in general. In addition, we use this connection to show how to derive the continuous variable Einstein-Podolsky-Rosen steering inequality with discrete measurements as seen in (Phys. Rev. Lett. 110 130407), and make an additional comment which strengthens this result.
In this Letter, we derive an entropic Einstein-Podolsky-Rosen (EPR) steering inequality for continuous-variable systems using only experimentally measured discrete probability distributions and details of the measurement apparatus. We use this inequality to witness EPR steering between the positions and momenta of photon pairs generated in spontaneous parametric down-conversion. We examine the asymmetry between parties in this inequality, and show that this asymmetry can be used to reduce the technical requirements of experimental setups intended to demonstrate the EPR paradox. Furthermore, we develop a more stringent steering inequality that is symmetric between parties, and use it to show that the down-converted photon pairs also exhibit symmetric EPR steering.
We formally link the concept of steering (a concept created by Schr\"odinger but only recently formalized by Wiseman, Jones, and Doherty [Phys. Rev. Lett. 98, 140402 (2007)]) and the criteria for demonstrations of Einstein-Podolsky-Rosen (EPR) paradox introduced by Reid [Phys. Rev. A 40, 913 (1989)]. We develop a general theory of experimental EPR-steering criteria, derive a number of criteria applicable to discrete as well as continuous-variable observables, and study their efficacy in detecting that form of nonlocality in some classes of quantum states. We show that previous versions of EPR-type criteria can be rederived within this formalism, thus unifying these efforts from a modern quantum-information perspective and clarifying their conceptual and formal origin. The theory follows in close analogy with criteria for other forms of quantum nonlocality (Bell nonlocality and entanglement), and because it is a hybrid of those two, it may lead to insights into the relationship between the different forms of nonlocality and the criteria that are able to detect them.
We show how one can demonstrate continuous-variable Einstein–Podolsky–Rosen (EPR) steering without needing to characterize entire measurement probability distributions. To do this, we develop a modified Fano inequality useful for discrete measurements of continuous variables and use it to bound the conditional uncertainties in continuous-variable entropic EPR-steering inequalities. With these bounds, we show how one can hedge against experimental limitations including a finite detector size, dead space between pixels, and any such factors that impose an incomplete sampling of the true measurement probability distribution. Furthermore, we use experimental data from the position and momentum statistics of entangled photon pairs in parametric downconversion to show that this method is sufficiently sensitive for practical use.
We use entropic uncertainty relations to formulate inequalities that witness Einstein-Podolsky-Rosen (EPR)-steering correlations in diverse quantum systems. We then use these inequalities to formulate symmetric EPR-steering inequalities using the mutual information. We explore the differing natures of the correlations captured by one-way and symmetric steering inequalities and examine the possibility of exclusive one-way steerability in two-qubit states. Furthermore, we show that steering inequalities can be extended to generalized positive operator-valued measures, and we also derive hybrid steering inequalities between alternate degrees of freedom.