# What is an example of a steerable state that does not violate a Bell's inequality?

I understand that if a state violates Bell's inequality, it must be steerable. The relationship goes like this: $$\text{violates Bell's inequality} \Longrightarrow \text{steerable} \Longrightarrow \text{entangled}.$$ For example, one of the Bell states $$|\Phi^+\rangle = \frac{1}{\sqrt{2}} (|00\rangle + |11\rangle)$$ violates Bell's inequality and hence it is steerable. What would be an example of a state that is steerable, but does not violate Bell's inequality?

• @NorbertSchuch $\rho$ Bell nonlocal implies $\rho$ steerable. I think the OP is just asking for an example of a steerable state that is not Bell nonlocal. Isn't that what is shown e.g. in Wiseman et al. (journals.aps.org/prl/abstract/10.1103/PhysRevLett.98.140402)? – glS May 8 at 12:42
• @glS Fair point, I got things mixed up. If I understand the abstract correctly the example should then be some Werner or isotropic state. – Norbert Schuch May 8 at 12:53