Exploring Multipartite Steering Effect Using Bell Operators

While Bell operators are exploited in detecting Bell nonlocality and entanglement classification, we demonstrate their usefulness in exploring Einstein–Podolsky–Rosen (EPR) steering, which represents the quantum correlation intermediate between entanglement and Bell nonlocality. We propose a task function that detects steerability of multi-qubit states in bipartite scenarios. A novel necessary and sufficient steering criterion is based on the superposition of the recursive Bell operators which are often employed for detecting Bell nonlocality. Utilizing the task function we can (i) reveal the one-to-one mapping relation between joint measurability and unsteerability, (ii) geometrically depict and compare the entanglement classification and the steering criteria and propose a geometrical measure, and (iii) compare the EPR steering with Bell nonlocality using an alternative task function. We extend the result to detect EPR steering for multi-qutrit cases and some numerical results are illustrated as examples. Finally, the steering criteria in a star-shaped quantum network is studied to see how the result is applied to a genuine multipartite steering case.

Almost Quantum Correlations are Inconsistent with Specker's Principle

Ernst Specker considered a particular feature of quantum theory to be especially fundamental, namely that pairwise joint measurability of sharp measurements implies their global joint measurability (vimeo.com/52923835). To date, Specker's principle seemed incapable of singling out quantum theory from the space of all general probabilistic theories. In particular, its well-known consequence for experimental statistics, the principle of consistent exclusivity, does not rule out the set of correlations known as almost quantum, which is strictly larger than the set of quantum correlations. Here we show that, contrary to the popular belief, Specker's principle cannot be satisfied in any theory that yields almost quantum correlations.