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:quant-ph/0611219 · Physical Review A

Experimental procedures for entanglement verification

S. J. van Enk, Norbert Lütkenhaus, Harry J. Kimble

Published May 15, 2007• 101 citations
arXivHTMLPDF

Abstract

We give an overview of different types of entanglement that can be generated in experiments, as well as of various protocols that can be used to verify or quantify entanglement. We propose several criteria that, we argue, should be applied to experimental entanglement verification procedures. Explicit examples demonstrate that not following these criteria will tend to result in overestimating the amount of entanglement generated in an experiment or in inferring entanglement when there is none. We distinguish protocols meant to refute or eliminate hidden-variable models from those meant to verify entanglement.

DOI
10.1103/physreva.75.052318

Related papers

Can measuring entanglement be easy?

S. J. van Enk

I raise some doubts concerning a protocol recently applied in an experiment (Walborn et al, Nature) to measure entanglement. The protocol is much simpler than other known entanglement-verification methods, but, I argue, needs assumptions (namely that the state generated is known and pure) that are too strong to be allowed and that are not justified in most experiments. An extension of the protocol suggested in quant-ph/0605250 is much harder to implement and still relies on assumptions not justified in entanglement-verification protocols, as demonstrated by an explicit example.

arXiv:quant-ph/0606017•Jun 1, 2006•3 citations

Entanglement and Its Verification: A Tutorial on Classical and Quantum Correlations

Enno Giese

Entanglement, a defining property of quantum mechanics in which two physical subsystems cannot be seen as independent entities, challenges our everyday experience and classical intuition. However, only such strong quantum correlations enable quantum technologies, including quantum computing or communication, while revealing the limits of our classical worldview by violating local realism. Given its importance in modern quantum science, we present this tutorial addressing the questions: What is entanglement, how does it differ from classical correlations, and how can it be experimentally verified? Using celebrated examples, such as Schrödinger's cat, we highlight the distinction between classical and quantum correlations and illustrate the definition of entangled and separable states. We review entanglement criteria by discussing Heisenberg-type uncertainty relations for continuous variables and the CHSH inequality for discrete systems. Focusing on concepts of quantum correlations and operational entanglement witnesses, we provide accessible tools and illustrative examples aimed at demystifying entanglement for a broad readership.

quant-pharXiv:2511.09507•Nov 13, 2025•0 citations

Reliable entanglement verification

Juan Miguel Arrazola, Oleg Gittsovich, John M. Donohue +3 more

Any experiment attempting to verify the presence of entanglement in a physical system can only generate a finite amount of data. The statement that entanglement was present in the system can thus never be issued with certainty, requiring instead a statistical analysis of the data. Because entanglement plays a central role in the performance of quantum devices, it is crucial to make statistical claims in entanglement verification experiments that are reliable and have a clear interpretation. In this work, we apply recent results by Christandl and Renner [Phys. Rev. Lett. 109, 120403 (2012)] to construct a reliable entanglement verification procedure based on the concept of confidence regions. The statements made do not require the specification of a prior distribution, the assumption of independent measurements, or the assumption of an independent and identically distributed source of states. Moreover, we develop numerical tools that are necessary to employ this approach in practice, rendering the procedure ready to be applied to current experiments. We demonstrate this technique by analyzing the data of a photonic experiment generating two-photon states whose entanglement is verified with the use of an accessible nonlinear witness.

arXiv:1302.1182•Physical Review A•Jun 24, 2013•18 citations

Criteria for Genuine Multiparticle Quantum Correlations

Bastian Jungnitsch

Entanglement is deemed a valuable resource for quantum computing and lies at the heart of quantum information. At the same time, current experiments are venturing into the realm of quantum systems consisting of many particles. In this book, different aspects of entanglement and non-locality in multiparticle systems are investigated. First, it presents an approach for an experimental verification of non-locality and entanglement with a high statistical significance. Second, a criterion for genuine multiparticle entanglement is introduced. Furthermore, this criterion also allows for a way of quantifying multiparticle entanglement. Analytical criteria for entanglement in a special class of quantum states, so-called graph states, are presented. These criteria turn out to be also necessary for entanglement in certain cases. Finally, ways of generalizing a non-local hidden-variable model proposed by Leggett are shown.

•Mar 14, 2012•0 citations

Strengthened Bell inequalities for entanglement verification

Pavel Lougovski, S. J. van Enk

Bell inequalities were meant to test quantum mechanics vs local hidden variable models, but can also be used to verify entanglement. For entanglement verification purposes one assumes the validity of quantum mechanics as well as quantum descriptions of one's measurements. With the help of these assumptions it is possible to derive a strengthened Bell inequality whose violation implies entanglement. We generalize known examples of such inequalities by relating the expectation value of the Bell operator to a particular quantitative measure of entanglement, namely, the negativity. Moreover, we obtain statistics illustrating the fact that violating a given (strengthened or not) Bell inequality is a much more rare feat for a quantum state of two qubits than it is to be entangled.

arXiv:0908.0267•Physical Review A•Sep 30, 2009•10 citations

Characterizing entanglement sources

Pavel Lougovski, S. J. van Enk

We discuss how to characterize entanglement sources with finite sets of measurements. The measurements do not have to be tomographically complete and may consist of POVMs rather than von Neumann measurements. Our method yields a probability that the source generates an entangled state as well as estimates of any desired calculable entanglement measures, including their error bars. We apply two criteria, namely, Akaike's information criterion and the Bayesian information criterion, to compare and assess different models (with different numbers of parameters) describing entanglement-generating devices. We discuss differences between standard entanglement-verification methods and our present method of characterizing an entanglement source.

arXiv:0908.0265•Physical Review A•Nov 18, 2009•11 citations
We give an overview of different types of entanglement that can be generated in experiments, as well as of various protocols that can be used to verify or quantify entanglement. We propose several criteria that, we argue, should be applied to experimental entanglement verification procedures. Explicit examples demonstrate that not following these criteria will tend to result in overestimating the amount of entanglement generated in an experiment or in inferring entanglement when there is none. We distinguish protocols meant to refute or eliminate hidden-variable models from those meant to verify entanglement.
I raise some doubts concerning a protocol recently applied in an experiment (Walborn et al, Nature) to measure entanglement. The protocol is much simpler than other known entanglement-verification methods, but, I argue, needs assumptions (namely that the state generated is known and pure) that are too strong to be allowed and that are not justified in most experiments. An extension of the protocol suggested in quant-ph/0605250 is much harder to implement and still relies on assumptions not justified in entanglement-verification protocols, as demonstrated by an explicit example.
Entanglement, a defining property of quantum mechanics in which two physical subsystems cannot be seen as independent entities, challenges our everyday experience and classical intuition. However, only such strong quantum correlations enable quantum technologies, including quantum computing or communication, while revealing the limits of our classical worldview by violating local realism. Given its importance in modern quantum science, we present this tutorial addressing the questions: What is entanglement, how does it differ from classical correlations, and how can it be experimentally verified? Using celebrated examples, such as Schrödinger's cat, we highlight the distinction between classical and quantum correlations and illustrate the definition of entangled and separable states. We review entanglement criteria by discussing Heisenberg-type uncertainty relations for continuous variables and the CHSH inequality for discrete systems. Focusing on concepts of quantum correlations and operational entanglement witnesses, we provide accessible tools and illustrative examples aimed at demystifying entanglement for a broad readership.
Any experiment attempting to verify the presence of entanglement in a physical system can only generate a finite amount of data. The statement that entanglement was present in the system can thus never be issued with certainty, requiring instead a statistical analysis of the data. Because entanglement plays a central role in the performance of quantum devices, it is crucial to make statistical claims in entanglement verification experiments that are reliable and have a clear interpretation. In this work, we apply recent results by Christandl and Renner [Phys. Rev. Lett. 109, 120403 (2012)] to construct a reliable entanglement verification procedure based on the concept of confidence regions. The statements made do not require the specification of a prior distribution, the assumption of independent measurements, or the assumption of an independent and identically distributed source of states. Moreover, we develop numerical tools that are necessary to employ this approach in practice, rendering the procedure ready to be applied to current experiments. We demonstrate this technique by analyzing the data of a photonic experiment generating two-photon states whose entanglement is verified with the use of an accessible nonlinear witness.
Entanglement is deemed a valuable resource for quantum computing and lies at the heart of quantum information. At the same time, current experiments are venturing into the realm of quantum systems consisting of many particles. In this book, different aspects of entanglement and non-locality in multiparticle systems are investigated. First, it presents an approach for an experimental verification of non-locality and entanglement with a high statistical significance. Second, a criterion for genuine multiparticle entanglement is introduced. Furthermore, this criterion also allows for a way of quantifying multiparticle entanglement. Analytical criteria for entanglement in a special class of quantum states, so-called graph states, are presented. These criteria turn out to be also necessary for entanglement in certain cases. Finally, ways of generalizing a non-local hidden-variable model proposed by Leggett are shown.
Bell inequalities were meant to test quantum mechanics vs local hidden variable models, but can also be used to verify entanglement. For entanglement verification purposes one assumes the validity of quantum mechanics as well as quantum descriptions of one's measurements. With the help of these assumptions it is possible to derive a strengthened Bell inequality whose violation implies entanglement. We generalize known examples of such inequalities by relating the expectation value of the Bell operator to a particular quantitative measure of entanglement, namely, the negativity. Moreover, we obtain statistics illustrating the fact that violating a given (strengthened or not) Bell inequality is a much more rare feat for a quantum state of two qubits than it is to be entangled.
We discuss how to characterize entanglement sources with finite sets of measurements. The measurements do not have to be tomographically complete and may consist of POVMs rather than von Neumann measurements. Our method yields a probability that the source generates an entangled state as well as estimates of any desired calculable entanglement measures, including their error bars. We apply two criteria, namely, Akaike's information criterion and the Bayesian information criterion, to compare and assess different models (with different numbers of parameters) describing entanglement-generating devices. We discuss differences between standard entanglement-verification methods and our present method of characterizing an entanglement source.