Teleportation fidelity as a probe of sub-Planck phase-space structure

TL;DR

This paper explores how the sub-Planck scale structures in the Wigner function influence the fidelity of continuous-variable quantum teleportation, linking quantum phase-space features to teleportation performance.

Contribution

It establishes a quantitative relationship between sub-Planck structures in the Wigner function and teleportation fidelity, including for mixed states and various quantum states.

Findings

High teleportation fidelity requires large squeezing to faithfully transmit sub-Planck structures.

Explicit relation between Wigner function's fine-scale structure and its large-scale extent.

Analysis of coherent, number, and chaotic states demonstrates the theory's applicability.

Abstract

We investigate the connection between sub-Planck structure in the Wigner function and the output fidelity of continuous-variable teleportation protocols. When the teleporting parties share a two-mode squeezed state as an entangled resource, high fidelity in the output state requires a squeezing large enough that the smallest sub-Planck structures in an input pure state are teleported faithfully. We formulate this relationship, which leads to an explicit relation between the fine-scale structure in the Wigner function and large-scale extent of the Wigner function, and we treat specific examples, including coherent, number, and random states and states produced by chaotic dynamics. We generalize the pure-state results to teleportation of mixed states.