Continuous-variable teleportation of a negative Wigner function

TL;DR

This paper investigates the conditions under which negativity of the Wigner function, a hallmark of non-classicality, can be teleported in continuous-variable quantum systems, revealing thresholds and advantages of conditional teleportation.

Contribution

It demonstrates that negativity of a single-photon state's Wigner function can be unconditionally teleported with arbitrarily weak squeezing, and analyzes the thresholds and performance of conditional teleportation.

Findings

Negativity can be unconditionally teleported with weak squeezing.

A strict squeezing threshold is required for teleporting attenuated single-photon states.

Conditional teleportation approaches perfect transmission at low squeezing but with reduced success rate.

Abstract

Teleportation is a basic primitive for quantum communication and quantum computing. We address the problem of continuous-variable (unconditional and conditional) teleportation of a pure single-photon state and a mixed attenuated single-photon state generally in a nonunity gain regime. Our figure of merit is the maximum of negativity of the Wigner function that witnesses highly non-classical feature of the teleported state. We find that negativity of the Wigner function of the single-photon state can be {\em unconditionally} teleported for arbitrarily weak squeezed state used to create the entangled state shared in the teleportation. In contrast, for the attenuated single-photon state there is a strict threshold squeezing one has to surpass in order to successfully teleport the negativity of its Wigner function. The {\em conditional} teleportation allows to approach perfect transmission of the single photon for an arbitrarily low squeezing at a cost of a success rate. On the other hand, for the attenuated single photon conditional teleportation cannot overcome the squeezing threshold of the unconditional teleportation and it approaches negativity of the input state only if the squeezing simultaneously increases. However, as soon as the threshold squeezing is surpassed the conditional teleportation still pronouncedly outperforms the unconditional one. The main consequences for quantum communication and quantum computing with continuous variables are discussed.