Uncertainty principle lies at the heart of quantum mechanics, while nonlocality is an intriguing phenomenon of quantum mechanics to rule out local causal theories. One subtle form of nonlocality is so-called Einstein-Podolsky-Rosen (EPR) steering, which holds the potential for shared entanglement verification even if the one-sided measurement device is untrusted. However, certifying EPR steering remains a big challenge presently. Here, we employ the local uncertainty relation to provide an experimental friendly approach for EPR steering verification. We show that the strength of EPR steering is quantitatively linked to the strength of the uncertainty relation, as well as the amount of entanglement. We find also that the realignment method works for detecting EPR steering of an arbitrary dimensional system.
Uncertainty principle lies at the heart of quantum mechanics, while nonlocality is an intriguing phenomenon of quantum mechanics to rule out local causal theories. One subtle form of nonlocality is so-called Einstein-Podolsky-Rosen (EPR) steering, which holds the potential for shared entanglement verification even if the one-sided measurement device is untrusted. However, certifying EPR steering remains a big challenge presently. Here, we employ the local uncertainty relation to provide an experimental friendly approach for EPR steering verification. We show that the strength of EPR steering is quantitatively linked to the strength of the uncertainty relation, as well as the amount of entanglement. We find also that the realignment method works for detecting EPR steering of an arbitrary dimensional system.
The Einstein-Podolsky-Rosen (EPR) steering is a subtle intermediate correlation between entanglement and Bell nonlocality. It not only theoretically completes the whole picture of non-local effects but also practically inspires novel quantum protocols in specific scenarios. However, a verification of EPR steering is still challenging due to difficulties in bounding unsteerable correlations. In this survey, the basic framework to study the bipartite EPR steering is discussed, and general techniques to certify EPR steering correlations are reviewed.
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.
The striking and distinctive nonlocal features of quantum mechanics were discovered by Einstein, Podolsky, and Rosen (EPR) beyond classical physics. At the core of the EPR argument, it was ``steering'' that Schr\"odinger proposed in 1935. Besides its fundamental significance, quantum steering opens up a novel application for quantum communication. Recent work has precisely characterized its properties; however, witnessing the EPR nonlocality remains a big challenge under arbitrary local measurements. Here we present an alternative linear criterion and complement existing results to efficiently testify steering for high-dimensional system in practice. By developing a novel and analytical method to tackle the maximization problem in deriving the bound of a steering criterion, we show how observed correlations can reveal powerfully the EPR nonlocality in an easily accessed manner. Although the criteria is not necessary and sufficient, it can recover some of the known results under a few settings of local measurements and is applicable even if the size of the system or the number of measurement settings are high. Remarkably, a deep connection is explicitly established between the steering and amount of entanglement. The results promise viable paths for secure communication with an untrusted source, providing optional loophole-free tests of the EPR nonlocality for high-dimensional states, as well as motivating solutions for other related problems in quantum information theory.
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.
Einstein-Podolsky-Rosen (EPR) steering is a form of quantum nonlocality which is intermediate between entanglement and Bell nonlocality. EPR steering is a resource for quantum key distribution that is device independent on only one side in that it certifies bipartite entanglement when one party's device is not characterized while the other party's device is fully characterized. In this work, we introduce two types of genuine tripartite EPR steering, and derive two steering inequalities to detect them. In a semi-device-independent scenario where only the dimensions of two parties are assumed, the correlations which violate one of these inequalities also certify genuine tripartite entanglement. It is known that Alice can demonstrate bipartite EPR steering to Bob if and only if her measurement settings are incompatible. We demonstrate that quantum correlations can also detect tripartite EPR steering from Alice to Bob and Charlie, even if Charlie's measurement settings are compatible.
The Einstein–Podolsky–Rosen (EPR) paradox is one of the milestones in quantum foundations, arising from the lack of a local realistic description of quantum mechanics. The EPR paradox has stimulated an important concept of “quantum nonlocality,” which manifests itself in three types: quantum entanglement, quantum steering, and Bell’s nonlocality. Although Bell’s nonlocality is more often used to show “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 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 friendlier for experimental implementation, i.e., one may measure the observables only in the 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 theoretical predictions. Our results deepen the understanding of quantum foundations and provide an efficient way to detect the steerability of quantum states.