Strong and uniform convergence in the teleportation simulation of bosonic Gaussian channels

Understand

In the literature on the continuous-variable bosonic teleportation protocol due to [Braunstein and Kimble, Phys.

• Rev.
• Lett., 80(4):869, 1998], it is often loosely stated that this protocol converges to a perfect teleportation of an input state in the limit of ideal squeezing and ideal detection, but the exact form of this convergence is typically not clarified.
• In this paper, I explicitly clarify that the convergence is in the strong sense, and not the uniform sense, and furthermore, that the convergence occurs for any input state to the protocol, including the infinite-energy Basel states defined and discussed here.