Quantum Steerability: Characterization, Quantification, Superactivation, and Unbounded Amplification
Chung-Yun Hsieh1*, Yeong-Cherng Liang2, Ray-Kuang Lee1,3
1Department of Physics, National Tsing Hua University, Hsinchu, Taiwan
2Department of Physics, National Cheng Kung University, Tainan, Taiwan
3Physics Division, National Center for Theoretical Science, Hsinchu, Taiwan
* presenting author:Chung-Yun Hsieh, email:andrew79106@yahoo.com.tw
Quantum steering, also called Einstein-Podolsky-Rosen steering, is the intriguing phenomenon associated with the ability of spatially separated observers to steer – by means of local measurements – the set of conditional quantum states accessible by a distant party. In the light of quantum information, all steerable quantum states are known to be resources for quantum information processing tasks. Here, via a quantity dubbed steering fraction, we derive a simple, but general criterion that allows one to identify quantum states that can exhibit quantum steering (without having to optimize over the measurements performed by each party), thus making an important step towards the characterization of steerable quantum states. The criterion, in turn, also provides upper bounds on the largest steering-inequality violation achievable by arbitrary finite-dimensional maximally entangled states. For the quantification of steerability, we prove that a strengthened version of the steering fraction is a convex steering monotone and demonstrate how it is related to two other steering monotones, namely, steerable weight and steering robustness. Using these tools, we further demonstrate the superactivation of steerability for a well-known family of entangled quantum states, i.e., we show how the steerability of certain entangled, but unsteerable quantum states can be recovered by allowing joint measurements on multiple copies of the same state. In particular, our approach allows one to explicitly construct a steering inequality to manifest this phenomenon. Finally, we prove that there exist examples of quantum states (including some which are unsteerable under projective measurements) whose steering-inequality violation can be arbitrarily amplified by allowing joint measurements on as little as three copies of the same state.

Keywords: Einstein-Podolsky-Rosen steering, Quantum steering, Superactivation