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:2312.05729 · Results in Physics

Parameterized steering criteria via correlation matrices

Qinghua Zhang, Le-Min Lai, Shao-Ming Fei

Published Dec 7, 2023• 1 citation
arXivHTMLPDF

Abstract

We study the steerability for arbitrary dimensional bipartite systems based on the correlation matrices given by local special unitary groups. We present families of steering criteria for bipartite quantum states in terms of parameterized correlation matrices. We show that these steering criteria may detect more steerable states than the existing steering criteria. The results are illustrated by detailed examples.

DOI
10.1016/j.rinp.2023.107253

Related papers

Detecting Einstein-Podolsky-Rosen steering via correlation matrices

Le-Min Lai, Shunlong Luo

Einstein-Podolsky-Rosen (EPR) steering is a kind of quantum nonlocal correlation characterizing the ability of one party to remotely affect another party's state by local measurements. It is regarded as an essential resource for one-sided device-independent quantum information processing. Although identification of EPR steerable states has been widely studied, it remains a hard issue under arbitrary local measurements. In this paper, we propose a steerability criterion for arbitrary dimensional bipartite systems via correlation matrices of local observables. In particular, we apply the steering criterion to three classes of local measurements which are of special significance: local orthogonal observables, mutually unbiased measurements, and general symmetric informationally complete measurements. We obtain some useful criteria that are operational and experimentally testable. We further illustrate the criteria through several examples, compare them with some steering criteria in the literature, and exhibit their power and advantages in certain cases.

Physical Review A•Oct 3, 2022•20 citations

Steering criteria via covariance matrices of local observables in arbitrary-dimensional quantum systems

Se-Wan Ji, Jaehak Lee, Jiyong Park +1 more

We derive steerability criteria applicable for both finite- and infinite-dimensional quantum systems using covariance matrices of local observables. We show that these criteria are useful to detect a wide range of entangled states particularly in high-dimensional systems and that the steering criterion for general $M\ifmmode\times\else\texttimes\fi{}N$ modes of continuous variables, known as Gaussian criterion but applicable also for non-Gaussian states, are obtained as a special case. Extending from the approach of entanglement detection via covariance matrices, our criteria are based on the local uncertainty principles incorporating the asymmetric nature of steering scenario. Specifically, we apply the formulation to the case of local orthogonal observables and obtain some useful criteria that can be readily computable, and testable in experiment, with no need for numerical optimization.

arXiv:1509.02550•Physical Review A•Dec 28, 2015•27 citations

Hierarchy of Steering Criteria Based on Moments for All Bipartite Quantum Systems

Ioannis Kogias, Paul Skrzypczyk, Daniel Cavalcanti +2 more

Einstein-Podolsky-Rosen steering is a manifestation of quantum correlations exhibited by quantum systems that allows for entanglement certification when one of the subsystems is not characterized. Detecting the steerability of quantum states is essential to assess their suitability for quantum information protocols with partially trusted devices. We provide a hierarchy of sufficient conditions for the steerability of bipartite quantum states of any dimension, including continuous variable states. Previously known steering criteria are recovered as special cases of our approach. The proposed method allows us to derive optimal steering witnesses for arbitrary families of quantum states and provides a systematic framework to analytically derive nonlinear steering criteria. We discuss relevant examples and, in particular, provide an optimal steering witness for a lossy single-photon Bell state; the witness can be implemented just by linear optics and homodyne detection and detects steering with a higher loss tolerance than any other known method. Our approach is readily applicable to multipartite steering detection and to the characterization of joint measurability.

arXiv:1507.04164•Physical Review Letters•Nov 17, 2015•127 citations

Computable steering criterion for bipartite quantum systems

Guo‐Zhu Pan, Jun‐Long Zhao, Zhi Lin +3 more

Quantum steering describes the ability of one observer to nonlocally affect the other observer's state through local measurements, which represents a new form of quantum nonlocal correlation and has potential applications in quantum information and quantum communication. In this paper, we propose a computable steering criterion that is applicable to bipartite quantum systems of arbitrary dimensions. The criterion can be used to verify a wide range of steerable states directly from a given density matrix without constructing measurement settings. Compared with the existing steering criteria, it is readily computable and testable in experiment, which can also be used to verify entanglement as all steerable quantum states are entangled.

arXiv:2010.01902•Oct 2, 2020•0 citations

Steerability criteria based on Heisenberg–Weyl observables

Le-Min Lai, Shunlong Luo

Abstract Einstein–Podolsky–Rosen (EPR) steering is an intermediate form of nonlocality which interpolates between entanglement and Bell nonlocality. It has been shown that EPR steerable states are fundamental resources for one-sided device-independent quantum information tasks. Nevertheless, distinguishing quantum steerable states from the unsteerable ones in general cases remains a big challenge under active studies. The generalized Bloch representation of density matrices in terms of the Heisenberg observables is a useful tool for analyzing characteristics of quantum systems and plays an important role in quantum information. In this work, the role of this representation in detection of EPR steering is studied. More specifically, based on the correlation matrices of the Heisenberg–Weyl observables, a family of steerability criteria for arbitrary dimensional bipartite systems are proposed. A large class of Hermitian operators, which can conveniently witness steering in some scenarios, are further provided. Finally, these criteria are illustrated through several examples, are compared with some existing ones, and their power and advantages are exhibited in certain cases.

Journal of Physics A Mathematical and Theoretical•Feb 20, 2023•4 citations

Quantum separability criteria for arbitrary-dimensional multipartite states

Ming Li, Jing Wang, Shao-Ming Fei +1 more

We present separability criteria for both bipartite and multipartite quantum states. These criteria include the criteria based on the correlation matrix and its generalized form as special cases. We show by detailed examples that our criteria are more powerful than the positive partial transposition criterion, the realignment criterion, and the criteria based on the correlation matrices.

arXiv:1402.4428•Physical Review A•Feb 18, 2014•59 citations
We study the steerability for arbitrary dimensional bipartite systems based on the correlation matrices given by local special unitary groups. We present families of steering criteria for bipartite quantum states in terms of parameterized correlation matrices. We show that these steering criteria may detect more steerable states than the existing steering criteria. The results are illustrated by detailed examples.
Einstein-Podolsky-Rosen (EPR) steering is a kind of quantum nonlocal correlation characterizing the ability of one party to remotely affect another party's state by local measurements. It is regarded as an essential resource for one-sided device-independent quantum information processing. Although identification of EPR steerable states has been widely studied, it remains a hard issue under arbitrary local measurements. In this paper, we propose a steerability criterion for arbitrary dimensional bipartite systems via correlation matrices of local observables. In particular, we apply the steering criterion to three classes of local measurements which are of special significance: local orthogonal observables, mutually unbiased measurements, and general symmetric informationally complete measurements. We obtain some useful criteria that are operational and experimentally testable. We further illustrate the criteria through several examples, compare them with some steering criteria in the literature, and exhibit their power and advantages in certain cases.
We derive steerability criteria applicable for both finite- and infinite-dimensional quantum systems using covariance matrices of local observables. We show that these criteria are useful to detect a wide range of entangled states particularly in high-dimensional systems and that the steering criterion for general $M\ifmmode\times\else\texttimes\fi{}N$ modes of continuous variables, known as Gaussian criterion but applicable also for non-Gaussian states, are obtained as a special case. Extending from the approach of entanglement detection via covariance matrices, our criteria are based on the local uncertainty principles incorporating the asymmetric nature of steering scenario. Specifically, we apply the formulation to the case of local orthogonal observables and obtain some useful criteria that can be readily computable, and testable in experiment, with no need for numerical optimization.
Einstein-Podolsky-Rosen steering is a manifestation of quantum correlations exhibited by quantum systems that allows for entanglement certification when one of the subsystems is not characterized. Detecting the steerability of quantum states is essential to assess their suitability for quantum information protocols with partially trusted devices. We provide a hierarchy of sufficient conditions for the steerability of bipartite quantum states of any dimension, including continuous variable states. Previously known steering criteria are recovered as special cases of our approach. The proposed method allows us to derive optimal steering witnesses for arbitrary families of quantum states and provides a systematic framework to analytically derive nonlinear steering criteria. We discuss relevant examples and, in particular, provide an optimal steering witness for a lossy single-photon Bell state; the witness can be implemented just by linear optics and homodyne detection and detects steering with a higher loss tolerance than any other known method. Our approach is readily applicable to multipartite steering detection and to the characterization of joint measurability.
Quantum steering describes the ability of one observer to nonlocally affect the other observer's state through local measurements, which represents a new form of quantum nonlocal correlation and has potential applications in quantum information and quantum communication. In this paper, we propose a computable steering criterion that is applicable to bipartite quantum systems of arbitrary dimensions. The criterion can be used to verify a wide range of steerable states directly from a given density matrix without constructing measurement settings. Compared with the existing steering criteria, it is readily computable and testable in experiment, which can also be used to verify entanglement as all steerable quantum states are entangled.
Abstract Einstein–Podolsky–Rosen (EPR) steering is an intermediate form of nonlocality which interpolates between entanglement and Bell nonlocality. It has been shown that EPR steerable states are fundamental resources for one-sided device-independent quantum information tasks. Nevertheless, distinguishing quantum steerable states from the unsteerable ones in general cases remains a big challenge under active studies. The generalized Bloch representation of density matrices in terms of the Heisenberg observables is a useful tool for analyzing characteristics of quantum systems and plays an important role in quantum information. In this work, the role of this representation in detection of EPR steering is studied. More specifically, based on the correlation matrices of the Heisenberg–Weyl observables, a family of steerability criteria for arbitrary dimensional bipartite systems are proposed. A large class of Hermitian operators, which can conveniently witness steering in some scenarios, are further provided. Finally, these criteria are illustrated through several examples, are compared with some existing ones, and their power and advantages are exhibited in certain cases.