Einstein-Podolsky-Rosen Steering: Its Geometric Quantification and Witness
Huan-Yu Ku1*, Shin-Liang Chen1, Costantino Budroni2, Adam Miranowicz3,4, Yueh-Nan Chen1,3,5, Franco Nori3,6
1Department of Physics, National Cheng Kung University, Tainan, Taiwan
2Institute for Quantum Optics and Quantum Information (IQOQI), Boltzmanngasse, Vienna, Australia
3CEMS, RIKEN, Wako-shi, Japan
4Faculty of Physics, Adam Mickiewicz University, Pozna┬┤n, Poland
5Physics Division, National Center for Theoretical Sciences, Hsinchu, Taiwan
6Department of Physics, The University of Michigan, Ann Arbor, Michigan, USA
* Presenter:Huan-Yu Ku
We propose a measure of quantum steerability, namely a convex steering monotone, based on the trace distance between a given assemblage and its corresponding closest assemblage admitting a local-hidden-state (LHS) model. We provide methods to estimate such a quantity, via lower and upper bounds, based on semidefinite programming. For a qubit-qubit quantum state, the above ideas also allow us to visualize various steerability properties of the state in the Bloch sphere via a surface called an LHS surface. In particular, some steerability properties can be obtained by comparing such an LHS surface with a corresponding quantum steering ellipsoid.

Keywords: Quantum information, EPR steering, non-locality, local hidden state, entanglement