One-to-One Correspondence between Deterministic Port-Based Teleportation and Unitary Estimation

Understand

Port-based teleportation is a variant of quantum teleportation, where the receiver can choose one of the ports in his part of the entangled state shared with the sender, but cannot apply other recovery operations.

• We show that the optimal fidelity of deterministic port-based teleportation (dPBT) using $N=n+1$ ports to teleport a $d$-dimensional state is equivalent to the optimal fidelity of $d$-dimensional unitary estimation using $n$ calls of the input unitary operation.
• From any given dPBT, we can explicitly construct the corresponding unitary estimation protocol achieving the same optimal fidelity, and vice versa.
• Using the obtained one-to-one correspondence between dPBT and unitary estimation, we derive the asymptotic optimal fidelity of port-based teleportation given by $1-O(d^4)N^{-2}\leq F \leq 1-\Omega(d^4)N^{-2}$, which improves the previously known result given by $1-O(d^5)N^{-2} \leq F \leq 1-\Omega(d^2) N^{-2}$.