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

Frontiers of Physics

Inequality relations for the hierarchy of quantum correlations in two-qubit systems

Xiao‐Gang Fan, Fa Zhao, Huan Yang, Fei Ming, Dong Wang, Ye Liu

Published Nov 16, 2022• 8 citations
Publisher

Abstract

Entanglement, quantum steering and Bell nonlocality can be used to describe the distinct quantum correlations of quantum systems. Because of their different characteristics and application fields, how to divide them quantitatively and accurately becomes particularly important. Based on the sufficient and necessary criterion for quantum steering of an arbitrary two-qubit T-state, we derive the inequality relations between quantum steering and entanglement as well as between quantum steering and Bell nonlocality for the T-state. Additionally, we have verified those relations experimentally.

DOI
10.1007/s11467-022-1222-x

Related papers

Mapping criteria between nonlocality and steerability in qudit-qubit systems and between steerability and entanglement in qubit-qudit systems

Changbo Chen, Changliang Ren, Xiang-Jun Ye +1 more

Entanglement, quantum steering, and nonlocality are distinct quantum correlations which are the resources behind various quantum information and quantum computation applications. However, a central question of determining the precise quantitative relation among them is still unresolved. Here we present a mapping criterion between Bell nonlocality and quantum steering in the bipartite qudit-qubit system, as well as a mapping criterion between quantum steering and quantum entanglement in the bipartite qubit-qudit system, starting from the fundamental concepts of quantum correlations. Precise quantitative mapping criteria are derived analytically. Such mapping criteria are independent of the form of the state. In particular, they cover several previous well-known research results which are only special cases in our simple mapping criteria.

arXiv:1810.10234•Physical Review A•Nov 12, 2018•31 citations

Estimating quantum steering and Bell nonlocality through quantum entanglement in two-photon systems

Huan Yang, Fa Zhao, Xiao‐Gang Fan +6 more

Quantum entanglement, quantum steering and Bell nonlocality, as significant quantum resources in the field of quantum information science, can achieve variously valuable quantum information tasks. Among of them, quantum entanglement and Bell nonlocality are the weakest and strongest nonlocal correlations, respectively. One can capture the quantum steering and Bell nonlocality via violating steering inequality and Bell inequality, respectively. In general, the detections of quantum steering and Bell nonlocality are strictly harder than entanglement detection. Here, based on steering inequality test and quantum state tomography, we attain various nonlocal correlations and experimentally demonstrate that the estimations of quantum steering and Bell nonlocality can be realized according to the quantum entanglement of the prepared two-photon test states. The estimated efficiency of quantum steering is stronger than the one of Bell nonlocality in this scenario, i.e., more steerable two-photon test states can be verified through quantum entanglement. In addition, quantum steering and Bell nonlocality are bounded by the corresponding upper and lower bounds, and these bounds cannot be punctured by all prepared two-photon states in experiment. These results are conducive to understand the relations among these nonlocal correlations.

Optics Express•Jul 27, 2021•14 citations

Hierarchy of average correlation, quantum steering and Bell nonlocality in two-qubit systems

Qinglong Tian, GUO Youneng

Abstract Nonclassicality is seen as an important physical resource and offers quantum advantages in modern quantum information processing. Motivated by recent work on the interplay between Bell nonlocality and nonclassicality quantified by average correlation [ Phys. Rev. Res. 5 023063 (2023)], in this paper we aim to establish the intrinsic relationship between the average correlation and the violation of the three-setting linear steering inequality for arbitrary two-qubit states. The results suggest that average correlation is closely related to the violation of the three-setting linear steering inequality, like its relationship with Bell inequality violation. Moreover, the dynamical behaviors of average correlation and steering are carefully analyzed under the influence of local unital and nonunital noisy channels. Particularly, for any two-qubit states, the hierarchy of average correlation-steering-Bell nonlocality is demonstrated by using the singular value decomposition theorem.

Chinese Physics B•May 11, 2026•0 citations

Relationship between average correlation and quantum steering for arbitrary two-qubit states

You-neng Guo, Xiangjun Chen, H. P. Peng +1 more

Quantum nonlocality and nonclassicality are two remarkable characteristics of quantum theory, and offer quantum advantages in some quantum information processing. Motivated by recent work on the interplay between nonclassicality quantified by average correlation [Tschaffon et al., Phys. Rev. Res. 5,023063 (2023)] and Bell nonlocality, in this paper we aim to establish the relationship between the average correlation and the violation of the three-setting linear steering inequality for two-qubit systems. Exact lower and upper bounds of average correlation versus steering are obtained, and the respective states which suffice those bounds are also characterized. For clarity of our presentation, we illustrate these results with examples from well-known classes of two-qubit states. Moreover, the dynamical behavior of these two quantifiers is carefully analyzed under the influence of local unital and nonunital noisy channels. The results suggest that average correlation is closely related to the violation of three-setting linear steering, like its relationship with Bell violation. Particularly, for a given class of states, the hierarchy of nonclassicality-steering-Bell nonlocality is demonstrated.

arXiv:2410.11219•Oct 15, 2024•0 citations

Hierarchy and robustness of multilevel two-time temporal quantum correlations

Dawid Maskalaniec, Karol Bartkiewicz

Quantum steering refers to correlations that can be classified as intermediate between entanglement and Bell nonlocality. Every state exhibiting Bell nonlocality exhibits also quantum steering and every state exhibiting quantum steering is also entangled. In low dimensional cases similar hierarchical relations have been observed between the temporal counterparts of these correlations. Here, we study the hierarchy of such temporal correlations for a general multilevel quantum system. We demonstrate that the same hierarchy holds for two definitions of state over time. In order to compare different types of temporal correlations, we show that temporal counterparts of Bell nonlocality and entanglement can be quantified with a temporal nonlocality robustness and temporal entanglement robustness. Our numerical result reveal that in contrast to temporal steering, for temporal nonlocality to manifest itself we require the initial state not to be in a completely mixed state.

arXiv:2106.02844•Jun 5, 2021•2 citations

Shareability of quantum steering and its relation with entanglement

Biswajit Paul, Kaushiki Mukherjee

Steerability is a characteristic of quantum correlations lying between entanglement and Bell nonlocality. Understanding how these steering correlations can be shared between different parties has profound applications in ensuring the security of quantum communication protocols. Here we show that at most two bipartite reduced states of a three-qubit state can violate the three-setting CJWR linear steering inequality, contrary to the two-setting linear steering inequality. This result explains that quantum steering correlations have limited shareability properties apart from the conventional 'nonshareable' monogamy constraint. In contrast to the two-measurement-setting scenario, the three-setting scenario turns out to be more useful for developing a deeper understanding of the shareability of tripartite steering correlations. Apart from the distribution of steering correlations, several relations between reduced bipartite steering, different measures of bipartite entanglement of reduced states, and genuine tripartite entanglement are presented here. The results enable the detection of different kinds of tripartite entanglement.

arXiv:2005.14375•Physical Review A•Nov 6, 2020•27 citations
Entanglement, quantum steering and Bell nonlocality can be used to describe the distinct quantum correlations of quantum systems. Because of their different characteristics and application fields, how to divide them quantitatively and accurately becomes particularly important. Based on the sufficient and necessary criterion for quantum steering of an arbitrary two-qubit T-state, we derive the inequality relations between quantum steering and entanglement as well as between quantum steering and Bell nonlocality for the T-state. Additionally, we have verified those relations experimentally.
Entanglement, quantum steering, and nonlocality are distinct quantum correlations which are the resources behind various quantum information and quantum computation applications. However, a central question of determining the precise quantitative relation among them is still unresolved. Here we present a mapping criterion between Bell nonlocality and quantum steering in the bipartite qudit-qubit system, as well as a mapping criterion between quantum steering and quantum entanglement in the bipartite qubit-qudit system, starting from the fundamental concepts of quantum correlations. Precise quantitative mapping criteria are derived analytically. Such mapping criteria are independent of the form of the state. In particular, they cover several previous well-known research results which are only special cases in our simple mapping criteria.
Quantum entanglement, quantum steering and Bell nonlocality, as significant quantum resources in the field of quantum information science, can achieve variously valuable quantum information tasks. Among of them, quantum entanglement and Bell nonlocality are the weakest and strongest nonlocal correlations, respectively. One can capture the quantum steering and Bell nonlocality via violating steering inequality and Bell inequality, respectively. In general, the detections of quantum steering and Bell nonlocality are strictly harder than entanglement detection. Here, based on steering inequality test and quantum state tomography, we attain various nonlocal correlations and experimentally demonstrate that the estimations of quantum steering and Bell nonlocality can be realized according to the quantum entanglement of the prepared two-photon test states. The estimated efficiency of quantum steering is stronger than the one of Bell nonlocality in this scenario, i.e., more steerable two-photon test states can be verified through quantum entanglement. In addition, quantum steering and Bell nonlocality are bounded by the corresponding upper and lower bounds, and these bounds cannot be punctured by all prepared two-photon states in experiment. These results are conducive to understand the relations among these nonlocal correlations.
Abstract Nonclassicality is seen as an important physical resource and offers quantum advantages in modern quantum information processing. Motivated by recent work on the interplay between Bell nonlocality and nonclassicality quantified by average correlation [ Phys. Rev. Res. 5 023063 (2023)], in this paper we aim to establish the intrinsic relationship between the average correlation and the violation of the three-setting linear steering inequality for arbitrary two-qubit states. The results suggest that average correlation is closely related to the violation of the three-setting linear steering inequality, like its relationship with Bell inequality violation. Moreover, the dynamical behaviors of average correlation and steering are carefully analyzed under the influence of local unital and nonunital noisy channels. Particularly, for any two-qubit states, the hierarchy of average correlation-steering-Bell nonlocality is demonstrated by using the singular value decomposition theorem.
Quantum nonlocality and nonclassicality are two remarkable characteristics of quantum theory, and offer quantum advantages in some quantum information processing. Motivated by recent work on the interplay between nonclassicality quantified by average correlation [Tschaffon et al., Phys. Rev. Res. 5,023063 (2023)] and Bell nonlocality, in this paper we aim to establish the relationship between the average correlation and the violation of the three-setting linear steering inequality for two-qubit systems. Exact lower and upper bounds of average correlation versus steering are obtained, and the respective states which suffice those bounds are also characterized. For clarity of our presentation, we illustrate these results with examples from well-known classes of two-qubit states. Moreover, the dynamical behavior of these two quantifiers is carefully analyzed under the influence of local unital and nonunital noisy channels. The results suggest that average correlation is closely related to the violation of three-setting linear steering, like its relationship with Bell violation. Particularly, for a given class of states, the hierarchy of nonclassicality-steering-Bell nonlocality is demonstrated.
Quantum steering refers to correlations that can be classified as intermediate between entanglement and Bell nonlocality. Every state exhibiting Bell nonlocality exhibits also quantum steering and every state exhibiting quantum steering is also entangled. In low dimensional cases similar hierarchical relations have been observed between the temporal counterparts of these correlations. Here, we study the hierarchy of such temporal correlations for a general multilevel quantum system. We demonstrate that the same hierarchy holds for two definitions of state over time. In order to compare different types of temporal correlations, we show that temporal counterparts of Bell nonlocality and entanglement can be quantified with a temporal nonlocality robustness and temporal entanglement robustness. Our numerical result reveal that in contrast to temporal steering, for temporal nonlocality to manifest itself we require the initial state not to be in a completely mixed state.
Steerability is a characteristic of quantum correlations lying between entanglement and Bell nonlocality. Understanding how these steering correlations can be shared between different parties has profound applications in ensuring the security of quantum communication protocols. Here we show that at most two bipartite reduced states of a three-qubit state can violate the three-setting CJWR linear steering inequality, contrary to the two-setting linear steering inequality. This result explains that quantum steering correlations have limited shareability properties apart from the conventional 'nonshareable' monogamy constraint. In contrast to the two-measurement-setting scenario, the three-setting scenario turns out to be more useful for developing a deeper understanding of the shareability of tripartite steering correlations. Apart from the distribution of steering correlations, several relations between reduced bipartite steering, different measures of bipartite entanglement of reduced states, and genuine tripartite entanglement are presented here. The results enable the detection of different kinds of tripartite entanglement.