TY - JOUR

T1 - Quantum steerability

T2 - Characterization, quantification, superactivation, and unbounded amplification

AU - Hsieh, Chung Yun

AU - Liang, Yeong Cherng

AU - Lee, Ray Kuang

N1 - Funding Information:
The authors acknowledge useful discussions with Nicolas Brunner, Daniel Cavalcanti, Flavien Hirsch, and Marco Tlio Quintino and helpful suggestions from an anonymous referee of AQIS2016. This work is supported by the Ministry of Education, Taiwan, R.O.C., through Aiming for the Top University Project granted to the National Cheng Kung University (NCKU), and by the Ministry of Science and Technology, Taiwan (Grants No. 104-2112-M-006-021-MY3 and No. 105-2628-M-007-003-MY4).
Publisher Copyright:
© 2016 American Physical Society.

PY - 2016/12/27

Y1 - 2016/12/27

N2 - 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. For completeness, we also demonstrate how the largest steering-inequality violation can be used to bound the largest Bell-inequality violation and derive, analogously, a simple sufficient condition for Bell nonlocality from the latter.

AB - 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. For completeness, we also demonstrate how the largest steering-inequality violation can be used to bound the largest Bell-inequality violation and derive, analogously, a simple sufficient condition for Bell nonlocality from the latter.

UR - http://www.scopus.com/inward/record.url?scp=85010053644&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85010053644&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.94.062120

DO - 10.1103/PhysRevA.94.062120

M3 - Article

AN - SCOPUS:85010053644

SN - 2469-9926

VL - 94

JO - Physical Review A

JF - Physical Review A

IS - 6

M1 - 062120

ER -