Abstract
We consider the Braunstein–Kimble protocol for continuous variable teleportation and its application for the simulation of bosonic channels. We discuss the convergence properties of this protocol under various topologies (strong, uniform, and bounded-uniform) clarifying some typical misinterpretations in the literature. We then show that the teleportation simulation of an arbitrary single-mode Gaussian channel is uniformly convergent to the channel if and only if its noise matrix has full rank. The various forms of convergence are then discussed within adaptive protocols, where the simulation error must be propagated to the output of the protocol by means of a “peeling” argument, following techniques from PLOB [S. Pirandola et al., Nat. Comm. 8, 15043 (2017)]. Finally, as an application of the peeling argument and the various topologies of convergence, we provide complete rigorous proofs for recently claimed strong converse bounds for private communication over Gaussian channels.Graphical abstract
Highlights
Quantum teleportation [1,2,3,4,5] is a fundamental operation in quantum information theory [6,7,8] and quantum Shannon theory [9,10]
It is a central tool for simulating quantum channels with direct applications to quantum/private communications [11] and quantum metrology [12]
We investigate the simulation of single-mode bosonic Gaussian channels, which can be fully classified in different canonical forms [68,69,70] up to input/output Gaussian unitaries
Summary
Quantum teleportation [1,2,3,4,5] is a fundamental operation in quantum information theory [6,7,8] and quantum Shannon theory [9,10]. Assuming various topologies of convergence (strong, uniform, and bounded-uniform), we study the teleportation simulation of bosonic channels in adaptive protocols. We discuss the crucial role of a peeling argument that connects the channel simulation error, associated with the single channel transmissions, to the overall simulation error accumulated on the final quantum state at the output of the protocol This argument is needed in order to rigorously prove strong converse upper bounds for two-way assisted private capacities. We show how the bounds claimed in WTB can be rigorously proven for adaptive protocols, and how their illness (divergence to infinity) is fixed by a correct use of the BK teleportation protocol In this regard, our study extends the one already given in reference [11] to include the topologies of strong and uniform convergence.
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