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Laser Physics Letters

Einstein–Podolsky–Rosen steering testing via quantum measurement

Jiadong Shi, Wen‐Yang Sun, Tao Wu

Published Sep 7, 2021• 1 citation
Publisher

Abstract

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.

DOI
10.1088/1612-202x/ac191d

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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
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.
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 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.
Einstein-Podolsky-Rosen (EPR) steering describes the ability of one observer to nonlocally "steer" the other observer's state through local measurements. EPR steering exhibits a unique asymmetric property; i.e., the steerability can differ between observers, which can lead to one-way EPR steering in which only one observer obtains steerability in the steering process. This property is inherently different from the symmetric concepts of entanglement and Bell nonlocality, and it has attracted increasing interest. Here, we experimentally demonstrate asymmetric EPR steering for a class of two-qubit states in the case of two measurement settings. We propose a practical method to quantify the steerability. We then provide a necessary and sufficient condition for EPR steering and clearly demonstrate one-way EPR steering. Our work provides new insight into the fundamental asymmetry of quantum nonlocality and has potential applications in asymmetric quantum information processing.
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.
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.