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

Self-teleportation and its application on LOCC estimation and other tasks