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Physical Review A

Einstein-Podolsky-Rosen steering and entanglement based on two-photon correlation for bipartite Gaussian states

Benyuan Zhou, Guoqing Yang, Gao‐xiang Li

Published Jun 6, 2019• 10 citations
Publisher

Abstract

We propose and demonstrate a standard form of Einstein-Podolsky-Rosen (EPR) steering for an arbitrary bipartite Gaussian state under which a simple EPR steering criterion for two-photon correlation can be achieved. In terms of a beam splitter preparing three different steerable states, we further test that the simplified criterion is reliable and efficient when it is used to determine whether an arbitrary bipartite Gaussian state is steerable or not. Based on the same theoretical framework, the standard form and criterion of entanglement are reconstructed and discussed. Furthermore, it is found that EPR steering requires stronger two-photon correlation than entanglement, while its direction is strictly dependent on the mean photon number of two light modes. Moreover, the inherent asymmetric feature can be intuitively embodied in the corresponding criteria, and the essential difference and inherent relation between two standard forms is revealed. We hope the present results could be helpful for potential applications in quantum information processing.

DOI
10.1103/physreva.99.062101

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We propose and demonstrate a standard form of Einstein-Podolsky-Rosen (EPR) steering for an arbitrary bipartite Gaussian state under which a simple EPR steering criterion for two-photon correlation can be achieved. In terms of a beam splitter preparing three different steerable states, we further test that the simplified criterion is reliable and efficient when it is used to determine whether an arbitrary bipartite Gaussian state is steerable or not. Based on the same theoretical framework, the standard form and criterion of entanglement are reconstructed and discussed. Furthermore, it is found that EPR steering requires stronger two-photon correlation than entanglement, while its direction is strictly dependent on the mean photon number of two light modes. Moreover, the inherent asymmetric feature can be intuitively embodied in the corresponding criteria, and the essential difference and inherent relation between two standard forms is revealed. We hope the present results could be helpful for potential applications in quantum information processing.
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.
Asymmetric Einstein–Podolsky–Rosen (EPR) steering means the ability of one party to nonlocally “steer” the state in the other side through local measurements. The asymmetric property of EPR steering provides adequate security in one-sided device-independent secure quantum communication protocols. In this paper, we theoretically investigate the asymmetric EPR steering schemes between two subsystems of multipartite entangled states by an asymmetric modulation method. Two schemes, including tripartite entangled state to bipartite steering and quadripartite entangled state to tripartite steering, are investigated. By reconstructing the covariance matrix of continuous variable multipartite Gaussian states, we quantify the steerability of manipulating two different subsystems and demonstrate the EPR steering parameter versus various types of states’ parameters. Our work provides a reference for asymmetric quantum information processing and enriches resources for secure quantum networks.
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.
EPR steering is a form of bipartite quantum correlation that is intermediate between entanglement and Bell nonlocality. It is detected via the violation of steering inequalities, which provide sufficient conditions for the steerability of quantum states. Furthermore, there is a sufficient criterion for guaranteeing that a two-qubit state is unsteerable. But there are some two qubit states that can not determine the steerability of the steering inequality and the sufficient criteria. Here we introduce a way of quantifying this phenomenon and use it to study the steerability of two qubit states. This article recommend a platonic solid measurement schemes. And then discuss the problem, namely expanding the scope of steerable, which guarantees that the state is steerable.
Abstract Einstein–Podolsky–Rosen (EPR) steering is a method that is used to analyze the physical inseparability of a quantum system state. Theoretically, the preferences of EPR steering behaviour in the inseparability detection can be suitably characterized by means of steering criterion. Here, we propose a scheme to test the EPR steering of a bipartite entangled state via quantum measurement. Based on the operation angles involved in the measurement, we derive a series of conditions that determine whether the EPR steering exists or not, and further prove that for the specific initial state the EPR steering can be tested. As an application, we apply our scheme to identify the steerability of the asymmetry state and Werner state, and the steering testing can be realized by adjusting the operation angles.
Einstein-Podolsky-Rosen (EPR) steering is a form of quantum correlation that exhibits a fundamental asymmetry in the properties of quantum systems. Given two observers, Alice and Bob, there are known to exist bipartite entangled states which are one-way steerable in the sense that Alice can steer Bob's state, but Bob cannot steer Alice's state. Here, we generalize this phenomenon to three parties and find a cyclic property of tripartite EPR steering. In particular, we identify a three-qubit state whose reduced bipartite states are one-way steerable for arbitrary projective measurements. Moreover, the three-qubit state has a cyclic steering property in the sense that by arranging the system in a triangular configuration the neighboring parties can steer each other's states only in the same (e.g., clockwise) direction. That is, Alice can steer Bob's state, Bob can steer Charlie's state, and Charlie can steer Alice's state, but not the other way around.