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

Mark M. Wilde
Phys. Rev. A 97, 062305 – Published 5 June 2018

Abstract

In the literature on the continuous-variable bosonic teleportation protocol due to Braunstein and Kimble [Phys. Rev. Lett. 80, 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. I then extend these uniform convergence results to particular multimode bosonic Gaussian channels. 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 nonasymptotic secret-key-agreement capacities. As a by-product of the discussion given here, I confirm the correctness of the proof of such bounds from my joint work with Berta and Tomamichel from [Wilde, Tomamichel, and Berta, IEEE Trans. Inf. Theory 63, 1792 (2017)]. Furthermore, I show that it is not necessary to invoke the energy-constrained diamond distance in order to confirm the correctness of this proof.

  • Figure
  • Figure
  • Figure
  • Received 22 December 2017
  • Revised 15 February 2018

DOI:https://doi.org/10.1103/PhysRevA.97.062305

©2018 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Mark M. Wilde

  • Hearne Institute for Theoretical Physics, Department of Physics and Astronomy, Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803, USA

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 97, Iss. 6 — June 2018

Reuse & Permissions
Access Options
CHORUS

Article Available via CHORUS

Download Accepted Manuscript
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review A

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×