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

Presenting Author: Mark Wilde, Louisiana State University

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. I also prove, in contrast to the above result, that the teleportation simulations of pure loss, thermal, pure amplifier, amplifier, and additive-noise channels converge both strongly and uniformly to the original channels, in the limit of ideal squeezing and detection for the simulations. For these channels, I give explicit uniform bounds on the accuracy of their teleportation simulations. These convergence statements have important implications for mathematical proofs that make use of the teleportation simulation of bosonic Gaussian channels, some of which have to do with bounding their non-asymptotic secret-key-agreement capacities.

Read this article online: https://arxiv.org/abs/1712.00145

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