  A way to characterize quantum nonlocality is to see difference in the figure
of merit between LOCC optimal protocol and globally optimal protocol in doing
certain task, e.g., state estimation, state discrimination, cloning and
broadcasting. Especially, we focus on the case where $n$ tensor of unknown
states.
  Our conclusion is that separable pure states are more non-local than
entangled pure states. More specifically, the difference in the figure of the
merit is exponentially small if the state is entangled, and the exponent is log
of the largest Schmidt coefficient. On the other hand, in many cases,
estimation of separable states by LOCC is worse than the global optimal
estimate by $O(\frac{1}{n})$.
  To show that the gap is exponentially small for entangled states, we propose
self-teleportation protocol as the key component of construct of LOCC
protocols. Objective of the protocol is to transfer Alice's part of quantum
information by LOCC, using intrinsic entanglement of $| \phi_{\theta}>
^{\otimes n}$ without using any extra resources. This protocol itself is of
interest in its own right.
