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:2404.04048 · Physical Review A

Stronger Einstein-Podolsky-Rosen steering inequalities to detect the boundary between quantum mechanics and classical models

Ruo-Chen Wang, Zhuo-Chen Li, Xing-Yan Fan, Xiang-Ru Xie, Hong-Hao Wei, Choo Hiap Oh, Jing‐Ling Chen

Published Nov 12, 2024• 1 citation
arXivHTMLPDF

Abstract

In quantum information, the Werner state is a benchmark to test the boundary between quantum mechanics and classical models. There have been three well-known critical values for the two-qubit Werner state, i.e., ${V}_{\mathrm{c}}^{\mathrm{E}}=1/3$ characterizing the boundary between the entanglement and separable model, ${V}_{\mathrm{c}}^{\mathrm{B}}=1/{K}_{G}(3)$ characterizing the boundary between Bell's nonlocality and the local-hidden-variable model, and ${V}_{\mathrm{c}}^{\mathrm{S}}=1/2$ characterizing the boundary between Einstein-Podolsky-Rosen (EPR) steering and the local-hidden-state model. So far, the problem of ${V}_{\mathrm{c}}^{\mathrm{E}}=1/3$ has been completely solved by an inequality involving in the positive-partial-transpose criterion, while the question of how to reveal the other two critical values by the inequality approach is still open. In this work, we focus on EPR steering, which is a form of quantum nonlocality intermediate between entanglement and Bell's nonlocality. By proposing the stronger $N$-setting linear EPR-steering inequalities, we have successfully obtained the desired value ${V}_{\mathrm{c}}^{\mathrm{S}}=1/2$ for the two-qubit Werner state, thus resolving the long-standing problem.

DOI
10.1103/physreva.110.052210

Related papers

Peres-type Criterion of Einstein-Podolsky-Rosen Steering for Two Qubits

Yu-Xuan Zhang, Jing-Ling Chen

Quantum nonlocality manifests in multipartite systems through entanglement, Bell's nonlocality, and Einstein-Podolsky-Rosen (EPR) steering. While Peres's positive-partial-transpose criterion provides a simple and powerful test for entanglement, a comparably elegant spectral criterion for detecting EPR steering remains an open challenge. In this work, we systematically explore whether a Peres-type criterion can be established for EPR steering in the two-qubit system. Focusing on rank-2 (including rank-1) states and the two-qubit Werner state, we analyze the eigenvalues of their partially transposed density matrices and construct a significant steering criterion based on symmetric combinations of these eigenvalues. We prove that this criterion serves as a necessary and sufficient condition for steerability for the Werner state, all two-qubit pure states, all two-qubit rank-2 states. Furthermore, we validate the criterion for higher-rank states (rank-3 and rank-4) and show that the results align with known steering inequalities. Our findings suggest a more unified framework for detecting quantum nonlocality via partial transposition and open avenues for further theoretical and numerical investigations into steering detection.

quant-pharXiv:2601.12085•Jan 20, 2026•0 citations

Exact Steering Bound for Two-Qubit Werner States

Yujie Zhang, Eric Chitambar

Whether positive operator-valued measures (POVMs) provide advantages in demonstrating Bell nonlocality has remained unknown, even in the simple scenario of Einstein-Podolsky-Rosen steering with noisy singlet state, known as Werner states. Here we resolve this long-standing open problem by constructing a local hidden state model for Werner states with any visibility r≤1/2 under general POVMs, thereby closing the so-called Werner gap. This construction is based on an exact measurement compatibility model for the set of all noisy POVMs and also provides a local hidden variable model for a larger range of Werner states than previously known.

arXiv:2309.09960•Physical Review Letters•Jun 17, 2024•20 citations

Detecting Einstein-Podolsky-Rosen steering through entanglement detection

Debarshi Das, Souradeep Sasmal, Sovik Roy

Quantum inseparabilities can be classified into three inequivalent forms: entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell's nonlocality. Bell-nonlocal states form a strict subset of EPR steerable states which also form a strict subset of entangled states. Recently, EPR steerable states have been shown to be fundamental resources for one-sided device-independent quantum information processing tasks and, hence, identification of EPR steerable states becomes important from foundational as well as informational theoretic perspectives. In the present paper, we propose a criterion to detect whether a given two-qubit state is EPR steerable. From an arbitrary given two-qubit state, another two-qubit state is constructed in such a way that the given state is EPR steerable if the new constructed state is entangled. Hence, EPR steerability of an arbitrary two-qubit state can be detected by detecting entanglement of the newly constructed state. Apart from providing a distinctive way to detect EPR steering without using any steering inequality, the present paper also provides an alternative way to avoid locality loopholes in EPR steering tests and to reduce the ``complexity cost'' present in experimentally detecting EPR steering. We also generalize our criteria to detect EPR steering of higher dimensional quantum states. Finally, we illustrate our result by using our proposed technique to detect EPR steerability of various families of mixed states.

arXiv:1808.07848•Physical Review A•May 13, 2019•33 citations

Bell's Nonlocality Can be Tested through Einstein-Podolsky-Rosen Steering

Jing‐Ling Chen, Xiang-Jun Ye

Quantum nonlocality has recently been classified into three distinct types: quantum entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell's nonlocality. Experimentally Bell's nonlocality is usually tested by quantum violation of the Clause-Horne-Shimony-Holt (CHSH) inequality in the two-qubit system. Bell's nonlocality is the strongest type of nonlocality, also due this reason Bell-test experiments have encountered both the locality loophole and the detection loophole for a very long time. As a weaker nonlocality, EPR steering naturally escapes from the locality loophole and is correspondingly easier to be demonstrated without the detection loophole. In this work, we trigger an extraordinary approach to investigate Bell's nonlocality, which is strongly based on the EPR steering. We present a theorem, showing that for any two-qubit state $τ$, if its mapped state $ρ$ is EPR steerable, then the state $τ$ must be Bell nonlocal. The result not only pinpoints a deep connection between EPR steering and Bell's nonlocality, but also sheds a new light to realize a loophole-free Bell-test experiment (without the CHSH inequality) through the violation of steering inequality.

arXiv:1510.06640•Oct 22, 2015•0 citations

A Steering Paradox for Einstein-Podolsky-Rosen Argument and its Extended Inequality

Tianfeng Feng, Changliang Ren, Qin Feng +4 more

The Einstein-Podolsky-Rosen (EPR) paradox is one of the milestones in quantum foundations, arising from the lack of local realistic description of quantum mechanics. The EPR paradox has stimulated an important concept of "quantum nonlocality", which manifests itself by three different types: quantum entanglement, quantum steering, and Bell nonlocality. Although Bell nonlocality is more often used to show the "quantum nonlocality", the original EPR paradox is essentially a steering paradox. In this work, we formulate the original EPR steering paradox into a contradiction equality,thus making it amenable to an experimental verification. We perform an experimental test of the steering paradox in a two-qubit scenario. Furthermore, by starting from the steering paradox, we generate a generalized linear steering inequality and transform this inequality into a mathematically equivalent form, which is more friendly for experimental implementation, i.e., one may only measure the observables in $x$-, $y$-, or $z$-axis of the Bloch sphere, rather than other arbitrary directions. We also perform experiments to demonstrate this scheme. Within the experimental errors, the experimental results coincide with the theoretical predictions. Our results deepen the understanding of quantum foundations and provide an efficient way to detect the steerability of quantum states.

arXiv:2004.04352•Apr 9, 2020•0 citations

Einstein-Podolsky-Rosen correlations and Bell correlations in the simplest scenario

Quan Quan, Huangjun Zhu, Heng Fan +1 more

Einstein-Podolsky-Rosen (EPR) steering is an intermediate type of quantum nonlocality which sits between entanglement and Bell nonlocality. A set of correlations is Bell nonlocal if it does not admit a local hidden variable (LHV) model, while it is EPR nonlocal if it does not admit a local hidden variable--local hidden state (LHV-LHS) model. It is interesting to know what states can generate EPR-nonlocal correlations in the simplest nontrivial scenario, that is, two projective measurements for each party sharing a two-qubit state. Here we show that a two-qubit state can generate EPR-nonlocal full correlations (excluding marginal statistics) in this scenario if and only if it can generate Bell-nonlocal correlations. If full statistics (including marginal statistics) is taken into account, surprisingly, the same scenario can manifest the simplest one-way steering and the strongest hierarchy between steering and Bell nonlocality. To illustrate these intriguing phenomena in simple setups, several concrete examples are discussed in detail, which facilitates experimental demonstration. In the course of study, we introduce the concept of restricted LHS models and thereby derive a necessary and sufficient semidefinite-programming criterion to determine the steerability of any bipartite state under given measurements. Analytical criteria are further derived in several scenarios of strong theoretical and experimental interest.

arXiv:1601.00962•Physical Review A•Jun 15, 2017•20 citations
In quantum information, the Werner state is a benchmark to test the boundary between quantum mechanics and classical models. There have been three well-known critical values for the two-qubit Werner state, i.e., VcE=1/3{V}_{\mathrm{c}}^{\mathrm{E}}=1/3VcE​=1/3 characterizing the boundary between the entanglement and separable model, VcB=1/KG(3){V}_{\mathrm{c}}^{\mathrm{B}}=1/{K}_{G}(3)VcB​=1/KG​(3) characterizing the boundary between Bell's nonlocality and the local-hidden-variable model, and VcS=1/2{V}_{\mathrm{c}}^{\mathrm{S}}=1/2VcS​=1/2 characterizing the boundary between Einstein-Podolsky-Rosen (EPR) steering and the local-hidden-state model. So far, the problem of VcE=1/3{V}_{\mathrm{c}}^{\mathrm{E}}=1/3VcE​=1/3 has been completely solved by an inequality involving in the positive-partial-transpose criterion, while the question of how to reveal the other two critical values by the inequality approach is still open. In this work, we focus on EPR steering, which is a form of quantum nonlocality intermediate between entanglement and Bell's nonlocality. By proposing the stronger NNN-setting linear EPR-steering inequalities, we have successfully obtained the desired value VcS=1/2{V}_{\mathrm{c}}^{\mathrm{S}}=1/2VcS​=1/2 for the two-qubit Werner state, thus resolving the long-standing problem.
Quantum nonlocality manifests in multipartite systems through entanglement, Bell's nonlocality, and Einstein-Podolsky-Rosen (EPR) steering. While Peres's positive-partial-transpose criterion provides a simple and powerful test for entanglement, a comparably elegant spectral criterion for detecting EPR steering remains an open challenge. In this work, we systematically explore whether a Peres-type criterion can be established for EPR steering in the two-qubit system. Focusing on rank-2 (including rank-1) states and the two-qubit Werner state, we analyze the eigenvalues of their partially transposed density matrices and construct a significant steering criterion based on symmetric combinations of these eigenvalues. We prove that this criterion serves as a necessary and sufficient condition for steerability for the Werner state, all two-qubit pure states, all two-qubit rank-2 states. Furthermore, we validate the criterion for higher-rank states (rank-3 and rank-4) and show that the results align with known steering inequalities. Our findings suggest a more unified framework for detecting quantum nonlocality via partial transposition and open avenues for further theoretical and numerical investigations into steering detection.
Whether positive operator-valued measures (POVMs) provide advantages in demonstrating Bell nonlocality has remained unknown, even in the simple scenario of Einstein-Podolsky-Rosen steering with noisy singlet state, known as Werner states. Here we resolve this long-standing open problem by constructing a local hidden state model for Werner states with any visibility r≤1/2 under general POVMs, thereby closing the so-called Werner gap. This construction is based on an exact measurement compatibility model for the set of all noisy POVMs and also provides a local hidden variable model for a larger range of Werner states than previously known.
Quantum inseparabilities can be classified into three inequivalent forms: entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell's nonlocality. Bell-nonlocal states form a strict subset of EPR steerable states which also form a strict subset of entangled states. Recently, EPR steerable states have been shown to be fundamental resources for one-sided device-independent quantum information processing tasks and, hence, identification of EPR steerable states becomes important from foundational as well as informational theoretic perspectives. In the present paper, we propose a criterion to detect whether a given two-qubit state is EPR steerable. From an arbitrary given two-qubit state, another two-qubit state is constructed in such a way that the given state is EPR steerable if the new constructed state is entangled. Hence, EPR steerability of an arbitrary two-qubit state can be detected by detecting entanglement of the newly constructed state. Apart from providing a distinctive way to detect EPR steering without using any steering inequality, the present paper also provides an alternative way to avoid locality loopholes in EPR steering tests and to reduce the ``complexity cost'' present in experimentally detecting EPR steering. We also generalize our criteria to detect EPR steering of higher dimensional quantum states. Finally, we illustrate our result by using our proposed technique to detect EPR steerability of various families of mixed states.
Quantum nonlocality has recently been classified into three distinct types: quantum entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell's nonlocality. Experimentally Bell's nonlocality is usually tested by quantum violation of the Clause-Horne-Shimony-Holt (CHSH) inequality in the two-qubit system. Bell's nonlocality is the strongest type of nonlocality, also due this reason Bell-test experiments have encountered both the locality loophole and the detection loophole for a very long time. As a weaker nonlocality, EPR steering naturally escapes from the locality loophole and is correspondingly easier to be demonstrated without the detection loophole. In this work, we trigger an extraordinary approach to investigate Bell's nonlocality, which is strongly based on the EPR steering. We present a theorem, showing that for any two-qubit state τττ, if its mapped state ρρρ is EPR steerable, then the state τττ must be Bell nonlocal. The result not only pinpoints a deep connection between EPR steering and Bell's nonlocality, but also sheds a new light to realize a loophole-free Bell-test experiment (without the CHSH inequality) through the violation of steering inequality.
The Einstein-Podolsky-Rosen (EPR) paradox is one of the milestones in quantum foundations, arising from the lack of local realistic description of quantum mechanics. The EPR paradox has stimulated an important concept of "quantum nonlocality", which manifests itself by three different types: quantum entanglement, quantum steering, and Bell nonlocality. Although Bell nonlocality is more often used to show the "quantum nonlocality", the original EPR paradox is essentially a steering paradox. In this work, we formulate the original EPR steering paradox into a contradiction equality,thus making it amenable to an experimental verification. We perform an experimental test of the steering paradox in a two-qubit scenario. Furthermore, by starting from the steering paradox, we generate a generalized linear steering inequality and transform this inequality into a mathematically equivalent form, which is more friendly for experimental implementation, i.e., one may only measure the observables in xxx-, yyy-, or zzz-axis of the Bloch sphere, rather than other arbitrary directions. We also perform experiments to demonstrate this scheme. Within the experimental errors, the experimental results coincide with the theoretical predictions. Our results deepen the understanding of quantum foundations and provide an efficient way to detect the steerability of quantum states.
Einstein-Podolsky-Rosen (EPR) steering is an intermediate type of quantum nonlocality which sits between entanglement and Bell nonlocality. A set of correlations is Bell nonlocal if it does not admit a local hidden variable (LHV) model, while it is EPR nonlocal if it does not admit a local hidden variable--local hidden state (LHV-LHS) model. It is interesting to know what states can generate EPR-nonlocal correlations in the simplest nontrivial scenario, that is, two projective measurements for each party sharing a two-qubit state. Here we show that a two-qubit state can generate EPR-nonlocal full correlations (excluding marginal statistics) in this scenario if and only if it can generate Bell-nonlocal correlations. If full statistics (including marginal statistics) is taken into account, surprisingly, the same scenario can manifest the simplest one-way steering and the strongest hierarchy between steering and Bell nonlocality. To illustrate these intriguing phenomena in simple setups, several concrete examples are discussed in detail, which facilitates experimental demonstration. In the course of study, we introduce the concept of restricted LHS models and thereby derive a necessary and sufficient semidefinite-programming criterion to determine the steerability of any bipartite state under given measurements. Analytical criteria are further derived in several scenarios of strong theoretical and experimental interest.