Optimized detection of steering via linear criteria for arbitrary-dimensional states

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.

Figure 1

The $p$ is the parameter of the three-dimensional isotropic state $\rho \left(p\right):=p|{\varphi }_3\rangle \langle {\varphi }_3|+(1-p)\mathbb{I}/9$, and the $n$ is the number of settings which Alice and Bob use. The black square point represents the lower bound for violating a steering equality when using $n$ settings to measure the state.