Abstract Einstein–Podolsky–Rosen (EPR) steering, as an asymmetric form of nonlocal correlations, is a crucial resource for one-sided device-independent quantum information tasks. Although many methods have been proposed to certify steering, efficient detection of EPR steerable states remains an important and difficult issue, and it is desirable to study it from as many angles as possible. In this work, a class of finite tight frames, equiangular tight frames, are applied to explore the problem of certifying EPR steering, where each frame can be used to construct a positive operator-valued measure. More specifically, based on two different forms of correlation matrices derived from equiangular tight frames, two steerability criteria that are readily computable for arbitrary dimensional bipartite systems are proposed. These criteria are illustrated via several detailed examples and their relative advantage is exhibited in certain cases.
Abstract Einstein–Podolsky–Rosen (EPR) steering, as an asymmetric form of nonlocal correlations, is a crucial resource for one-sided device-independent quantum information tasks. Although many methods have been proposed to certify steering, efficient detection of EPR steerable states remains an important and difficult issue, and it is desirable to study it from as many angles as possible. In this work, a class of finite tight frames, equiangular tight frames, are applied to explore the problem of certifying EPR steering, where each frame can be used to construct a positive operator-valued measure. More specifically, based on two different forms of correlation matrices derived from equiangular tight frames, two steerability criteria that are readily computable for arbitrary dimensional bipartite systems are proposed. These criteria are illustrated via several detailed examples and their relative advantage is exhibited in certain cases.
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.
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.
Einstein-Podolsky-Rosen (EPR) steering, as a new form of nonlocality, stands between entanglement and Bell nonlocality, implying promising applications for quantum information tasks. The problem of detecting EPR steering plays an important role in characterization of quantum nonlocality. Despite some significant progress, one still faces a practical issue: how to detect EPR steering in an experimentally friendly fashion. Resorting to an EPR steering inequality, one is required to apply a strategy as efficiently as possible for any selected measurement settings on the two subsystems, one of which may not be trusted. Inspired by the recent powerful linear criteria proposed by Saunders et al. [D. J. Saunders, S. J. Jones, H. M. Wiseman, and G. J. Pryde, Nat. Phys. 6, 845 (2010).], we present an optimized method of certifying steering for an arbitrary-dimensional state in a cost-effective manner. We provide a practical way to signify steering via only a few settings to optimally violate the steering inequality. Our method leads to steering detections in a highly efficient way, and can be performed with any number of settings, for an arbitrary bipartite mixed state, which can reduce experimental overheads significantly.
Abstract Einstein–Podolsky–Rosen (EPR) steering represents a fundamental quantum resource in measurement theory and quantum information processing. However, determining steerability under general quantum measurements remains a challenging task, as existing methods often suffer from limitations such as high computational complexity, restricted applicability to low-dimensional systems, or dependence on specific classes of quantum states. To address this challenge, inspired by Lai and Luo (2022 Phys. Rev. A 106 042402) we propose a unified framework based on a class of informationally complete symmetric measurements. This framework naturally integrates established measurement paradigms, including mutually unbiased measurements and general symmetric informationally complete positive operator-valued measures, while offering enhanced versatility and flexibility. By leveraging the inherent mathematical symmetry of these measurements, we derive practical criteria for EPR steering through correlation matrices. Furthermore, the effectiveness of the proposed framework is rigorously validated on isotropic states, Werner states, and a 3 × 3 asymmetric state, respectively. As a result, this approach is both versatile and computationally efficient, significantly enhancing the ability to detect EPR steering and demonstrating strong potential for practical implementation in experimental quantum information protocols.
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.
Abstract Entanglement and Einstein–Podolsky–Rosen (EPR) steering are nonlocal quantum correlations, which are relevant resources for quantum information protocols. EPR steering, or quantum steering, refers to the correlation where a party might ‘steer’, or modify, the state of another, which is spatially separated. Entanglement is a symmetric resource while steering is asymmetrical, since it depends on the direction of the effect. Due to these different characteristics and the therefore different possible applications, there has been both theoretical and experimental research on forms to certify the distinct quantum nonlocal correlations. In recent years, alongside the investigation on quantum correlations between two systems, there has been a great interest in investigating multipartite/multimode entanglement as well as steering, since they include a high dimension and it may be possible to store more information than in a single qubit. In this review, we will summarize the different criteria and measures that have been developed for the characterization of these two kinds of correlations. We first focus on bipartite entanglement and steering. We then review the progress that has been made in the investigation of multipartite quantum correlations. We revise the theoretical work in quantum nonlocal correlation witnesses and measures, which respectively allow one to certify that the system is entangled or presents EPR steering, and give a quantification of the content of these correlations in the system. Then, we briefly review the experiments that have been designed and that demonstrate multipartite quantum correlations. We also include applications in quantum information protocols, in particular in quantum teleportation and quantum cryptography.