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

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.