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/0301030 · Physical Review Letters

Comprehensive Test of Entanglement for Two-Level Systems via the Indeterminacy Relationship

Sixia Yu, Jian-Wei Pan, Zeng‐Bing Chen, Yong-De Zhang

Published Nov 20, 2003• 37 citations
arXivHTMLPDF

Abstract

A 3-setting Bell-type inequality enforced by the indeterminacy relation of complementary local observables is proposed as an experimental test of 2-qubit entanglement. The proposed inequality has the advantage of being a sufficient and necessary criterion of separability. Therefore any entangled 2-qubit state cannot escape the detection by this kind of test. It turns out that the orientation of the local testing observables plays a crucial role in our perfect detection of entanglement.

DOI
10.1103/physrevlett.91.217903

Related papers

Detection of entanglement and Bell's inequality violation

Kai Chen, Ling-An Wu

We propose a new method for detecting entanglement of two qubits and discuss its relation with the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality. Without the need for full quantum tomography for the density matrix we can experimentally detect the entanglement by measuring less than 9 local observables for any given state. We show that this test is stronger than the CHSH-Bell inequality and also gives an estimation for the degree of entanglement. If prior knowledge is available we can further greatly reduce the number of required local observables. The test is convenient and feasible with present experimental technology.

arXiv:quant-ph/0306137•Jun 20, 2003•1 citation

Correlation criteria for Bell type inequalities and entanglement detection

Che‐Ming Li, Li‐Yi Hsu, Weiyang Lin +3 more

We provide a novel criterion for identifying quantum correlation, which allows us to find connections between Bell type inequalities, entanglement detection, and correlation. We utilize the criterion to construct witness operators that can detect genuine multi-qubit entanglement with fewer local measurements. The connection between identifications of quantum correlation and Mermin's inequality is discussed. Detection of genuine four-level tripartite entanglement with two local measurement settings is shown in the same manner. Further, through the criterion of quantum correlation, we derive a new Bell inequality for arbitrary high-dimensional bipartite systems, which requires fewer analyses of the measured outcomes.

arXiv:quant-ph/0607190•Jul 27, 2006•0 citations

Entanglement detection via the condition of quantum correlation

Che‐Ming Li, Li-Yi Hsu, Yueh-Nan Chen +2 more

We develop a necessary condition of quantum correlation. It is utilized to construct a $d$-level bipartite Bell-type inequality which is strongly resistant to noise and requires only analyses of $O(d)$ measurement outcomes compared to the previous result $O({d}^{2})$. Remarkably, a connection between the arbitrary high-dimensional bipartite Bell-type inequality and entanglement witnesses is found. Through the necessary condition of quantum correlation, we propose that the witness operators to detect truly multipartite entanglement for a generalized Greenberger-Horne-Zeilinger (GHZ) state with two local measurement settings and a four-qubit singlet state with three settings. Moreover, we also propose a robust entanglement witness to detect a four-level tripartite GHZ state with only two local measurement settings.

arXiv:0709.1982•Physical Review A•Sep 12, 2007•3 citations

Minimum detection efficiencies for a loophole-free observable-asymmetric Bell-type test

Gianni Garbarino

We discuss the problem of finding the most favorable conditions for closing the detection loophole in a test of local realism with a Bell inequality. For a generic nonmaximally entangled two-qubit state and two incompatible bases to be adopted for alternative measurements of two observables $\mathrm{a\ifmmode \hat{}\else \^{}\fi{}}$ and $\mathrm{b\ifmmode \hat{}\else \^{}\fi{}}$ on each party, we apply Hardy's proof of nonlocality without inequality and derive an Eberhard-like inequality. For an infinity of nonmaximally entangled states we find that it is possible to refute local realism by requiring perfect detection efficiency for only one of the two observables, say $\mathrm{b\ifmmode \hat{}\else \^{}\fi{}}$, to be measured on each party: The test is free from the detection loophole for any value of the detection efficiency corresponding to the other observable $\mathrm{a\ifmmode \hat{}\else \^{}\fi{}}$. The maximum tolerable noise in such a loophole-free observable-asymmetric test is also evaluated.

arXiv:0912.2258•Physical Review A•Mar 8, 2010•18 citations

Inequalities detecting quantum entanglement for 2⊗d systems

Ming‐Jing Zhao, Teng Ma, Shao-Ming Fei +1 more

We present a set of inequalities for detecting quantum entanglement of $2\ensuremath{\bigotimes}d$ quantum states. For $2\ensuremath{\bigotimes}2$ and $2\ensuremath{\bigotimes}3$ systems, the inequalities give rise to sufficient and necessary separability conditions for both pure and mixed states. For the case of $d>3$, these inequalities are necessary conditions for separability, which detect all entangled states that are not positive under partial transposition and even some entangled states with positive partial transposition. These inequalities are given by mean values of local observables and present an experimental way of detecting the quantum entanglement of $2\ensuremath{\bigotimes}d$ quantum states and even multiqubit pure states.

arXiv:1105.4668•Physical Review A•May 23, 2011•20 citations

Identification of three-qubit entanglement

Ming‐Jing Zhao, Ting-Gui Zhang, Xianqing Li‐Jost +1 more

We present a way of identifying all kinds of entanglement for three-qubit pure states in terms of the expectation values of Pauli operators. The necessary and sufficient conditions to classify the fully separable, biseparable, and genuine entangled states are explicitly given. The approach can be generalized to multipartite high-dimensional cases. For three-qubit mixed states, we propose two kinds of inequalities in terms of the expectation values of complementary observables. One inequality has advantages in entanglement detection of the quantum state with positive partial transpositions, and the other is able to detect genuine entanglement. The results give an effective method for experimental entanglement identification.

arXiv:1301.4317•Physical Review A•Jan 17, 2013•28 citations
A 3-setting Bell-type inequality enforced by the indeterminacy relation of complementary local observables is proposed as an experimental test of 2-qubit entanglement. The proposed inequality has the advantage of being a sufficient and necessary criterion of separability. Therefore any entangled 2-qubit state cannot escape the detection by this kind of test. It turns out that the orientation of the local testing observables plays a crucial role in our perfect detection of entanglement.
We propose a new method for detecting entanglement of two qubits and discuss its relation with the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality. Without the need for full quantum tomography for the density matrix we can experimentally detect the entanglement by measuring less than 9 local observables for any given state. We show that this test is stronger than the CHSH-Bell inequality and also gives an estimation for the degree of entanglement. If prior knowledge is available we can further greatly reduce the number of required local observables. The test is convenient and feasible with present experimental technology.
We provide a novel criterion for identifying quantum correlation, which allows us to find connections between Bell type inequalities, entanglement detection, and correlation. We utilize the criterion to construct witness operators that can detect genuine multi-qubit entanglement with fewer local measurements. The connection between identifications of quantum correlation and Mermin's inequality is discussed. Detection of genuine four-level tripartite entanglement with two local measurement settings is shown in the same manner. Further, through the criterion of quantum correlation, we derive a new Bell inequality for arbitrary high-dimensional bipartite systems, which requires fewer analyses of the measured outcomes.
We develop a necessary condition of quantum correlation. It is utilized to construct a ddd-level bipartite Bell-type inequality which is strongly resistant to noise and requires only analyses of O(d)O(d)O(d) measurement outcomes compared to the previous result O(d2)O({d}^{2})O(d2). Remarkably, a connection between the arbitrary high-dimensional bipartite Bell-type inequality and entanglement witnesses is found. Through the necessary condition of quantum correlation, we propose that the witness operators to detect truly multipartite entanglement for a generalized Greenberger-Horne-Zeilinger (GHZ) state with two local measurement settings and a four-qubit singlet state with three settings. Moreover, we also propose a robust entanglement witness to detect a four-level tripartite GHZ state with only two local measurement settings.
We discuss the problem of finding the most favorable conditions for closing the detection loophole in a test of local realism with a Bell inequality. For a generic nonmaximally entangled two-qubit state and two incompatible bases to be adopted for alternative measurements of two observables $\mathrm{a\ifmmode \hat{}\else \^{}\fi{}}$ and $\mathrm{b\ifmmode \hat{}\else \^{}\fi{}}$ on each party, we apply Hardy's proof of nonlocality without inequality and derive an Eberhard-like inequality. For an infinity of nonmaximally entangled states we find that it is possible to refute local realism by requiring perfect detection efficiency for only one of the two observables, say $\mathrm{b\ifmmode \hat{}\else \^{}\fi{}}$, to be measured on each party: The test is free from the detection loophole for any value of the detection efficiency corresponding to the other observable $\mathrm{a\ifmmode \hat{}\else \^{}\fi{}}$. The maximum tolerable noise in such a loophole-free observable-asymmetric test is also evaluated.
We present a set of inequalities for detecting quantum entanglement of $2\ensuremath{\bigotimes}d$ quantum states. For $2\ensuremath{\bigotimes}2$ and $2\ensuremath{\bigotimes}3$ systems, the inequalities give rise to sufficient and necessary separability conditions for both pure and mixed states. For the case of d>3d>3d>3, these inequalities are necessary conditions for separability, which detect all entangled states that are not positive under partial transposition and even some entangled states with positive partial transposition. These inequalities are given by mean values of local observables and present an experimental way of detecting the quantum entanglement of $2\ensuremath{\bigotimes}d$ quantum states and even multiqubit pure states.
We present a way of identifying all kinds of entanglement for three-qubit pure states in terms of the expectation values of Pauli operators. The necessary and sufficient conditions to classify the fully separable, biseparable, and genuine entangled states are explicitly given. The approach can be generalized to multipartite high-dimensional cases. For three-qubit mixed states, we propose two kinds of inequalities in terms of the expectation values of complementary observables. One inequality has advantages in entanglement detection of the quantum state with positive partial transpositions, and the other is able to detect genuine entanglement. The results give an effective method for experimental entanglement identification.