Abstract Steering, a quantum property stronger than entanglement but weaker than non-locality in the quantum correlation hierarchy, is a key resource for one-sided device-independent quantum key distribution applications, in which only one of the communicating parties is trusted. A fine-grained steering inequality was introduced in (2014 Phys. Rev. A 90 050305), enabling for the first time the detection of steering in all steerable two-qubit Werner states using only two measurement settings. Here, we numerically and experimentally investigate this inequality for generalized Werner states and successfully detect steerability in a wide range of two-photon polarization-entangled Bell local states generated by a parametric down-conversion source.
Quantum steering, as a cornerstone of quantum information, is usually used to witness the quantum correlation of bipartite and multi-partite states. Here, we experimentally demonstrate the quantum steering inequality of two-qubit mixed states based on the fine-grained uncertainty relation. Our experimental results show that the steering inequality has potent sensitivity to Werner states and Bell diagonal states. The steering strategy exhibits a strong ability to identify that Werner states are steerable when the decoherence coefficient a>12. Compared to the steering inequality obtained by another stratagem, the steering witness criteria of mixed states based on the fine-grained uncertainty relation demonstrated in our experiment has better precision and accuracy. Moreover, the detection efficiency in our measurement setup is only required to be 50% to close the detection loophole, which means our approach needs less detector efficiency to certificate the steerability of mixed states.
We derive a steering inequality based on a fine-grained uncertainty relation to capture Einstein-Podolsky-Rosen steering for bipartite systems. Our steering inequality improves over previous ones since it can experimentally detect all steerable two-qubit Werner state with only two measurement settings on each side. According to our inequality, pure entangled states are maximally steerable. Moreover, by slightly changing the setting, we can express the amount of violation of our inequality as a function of their violation of the Clauser-Horne-Shimony-Holt inequality. Finally, after deriving a monogamy relation we prove that the amount of violation of our steering inequality is, up to a constant factor, a lower bound on the key rate of a one-sided device-independent quantum key distribution protocol secure against individual attacks.
Quantum steering is one form of quantum correlations interpolating between entanglement and Bell nonlocality, which in some cases can be detected by various steering inequalities. Recently, a remarkable and useful steerability criterion via geometric Bell-like inequalities was established [M. Zukowski, A. Dutta, and Z. Yin, Phys. Rev. A 91, 032107 (2015)]. We report an experimental investigation of this steering criterion and verify the geometric Bell-like steering inequality experimentally by using of the Werner states. The results demonstrate that the geometric Bell-like steering inequality is a convenient tool to detect quantum steering both theoretically and practically.
The steerability of a quantum state can be detected by steering inequalities. The linear steering inequalities show that more steerable states can be discovered with the increase of measurements. In order to detect more steerable states in two-photon systems, we first theoretically derive an optimized steering criterion based on infinity measurements for an arbitrary two-qubit state. The steering criterion is only determined by the spin correlation matrix of the state, and do not require infinity measurements. Then, we prepared the Werner-like states in two-photon systems, and measure their spin correlation matrices. Finally, we apply three steering criteria, which include our steering criterion, the three-measurement steering criterion and the geometric Bell-like inequality, to distinguish the steerability of these states. The results show that our steering criterion can detect the most steerable states under the same experimental conditions. Thus, our work provides a valuable reference for detecting the steerability of quantum states.
Quantum steering is the ability that one system affects another one without delay by performing local measurements. During the past few years, the research on quantum steering has been verified in a number of experiments by the choices of measurements. But this research cannot detect all steerable states. Recently, the definition of critical radius was proposed by Nguyen et al. [Phys. Rev. Lett. 122, 240401 (2019)]. The critical radius can detect all steerable states for two-qubit states. Therefore the critical radius can be regarded as the best method for detecting the steerability of two-qubit states. However, relevant experimental research is still lacking. In this work, for comparison, we experimentally investigate three steering criteria based on the critical radius, the geometric Bell-like inequality, and the three-setting measurements steering inequality and find that the critical radius can detect the most steerable states. Furthermore, we demonstrate that the critical radius satisfies the scaling property. The results show that we only need to calculate the critical radii of some quantum states to obtain the critical radii of more scaling quantum states. Thus this property can provide the convenience for detecting the steerability of many quantum states.
Phenomena that slip beyond the grasp of our classical intuition reveal uniquely quantum effects that deepen our understanding of the physical world and enable advances in information processing, particularly in quantum communication and computation. One such phenomenon is quantum steering, whereby measurements performed by one party influence the conditional states of another when the two share an entangled quantum system. If the observed correlations cannot be explained by a local hidden state model, the state is said to be steerable. In this work, we investigate the typicality of this behavior: given a generic two-qubit state and
m Haar-random projective measurements, what is the probability of observing steering? We derive analytical expressions for the steering probability
PS of Werner states in two- and three-setting scenarios, the latter restricted to coplanar projective measurements on the Bloch sphere. For larger numbers of settings and various random states ensembles, we perform numerical analyses showing that
PS increases systematically with the number of measurements and substantially exceeds the corresponding probabilities associated with Bell nonlocality. Our results demonstrate that random states with minimal environmental coupling exhibit a high probability of steering for finite
m and approach genuine typicality,
PS=100%, as the number of settings increases. We provide a detailed characterization of
PS across different state ensembles and specific families, including Bell-diagonal and Werner states, identifying those with the greatest non-classical potential and highlighting their relevance for protocols in which steering serves as a key resource.