Robust Gaussian Teleportation with Attenuations and Non-unity Gain

TL;DR

This paper analyzes the fidelity of Gaussian quantum teleportation under local attenuations and variable gain, establishing conditions for robust, genuinely quantum teleportation linked to entanglement properties.

Contribution

It introduces a comprehensive analysis of teleportation fidelity considering local attenuations and gain tuning, connecting robustness conditions to entanglement criteria.

Findings

Robust teleportation conditions depend on gain and local attenuations.

Robustness is equivalent to Gaussian bipartite entanglement properties.

Transformations preserving fidelity are characterized for Gaussian operations.

Abstract

The average fidelity of the teleportation of a coherent state is calculated for general Gaussian bipartite systems shared by the partners of the protocol, Alice and Bob. It is considered that the shared Gaussian bipartite modes suffer independent attenuations before the processing of Alice and Bob. Moreover the classical communication between the partners can be controlled by a gain not necessarily unitary. Comparing with the classical fidelity threshold of measure-and-prepare methods, we establish several genuinely quantum teleportation conditions which depend on the gain and the local attenuations. Considering that the gain can be tuned to maximize the bipartite state set able to genuinely quantum teleportation, a condition for teleportation robust to local attenuations is found. This condition is demonstrated to be essentially equivalent to the condition of robust Gaussian bipartite entanglement, obtained in previous articles, showing that the attenuation robustness is an entanglement property relevant for characterization and application of bipartite systems. For the derivation of the robust teleportation conditions, the Gaussian operations onto the bipartite system are thoroughly studied, so that the transformations that maintain the fidelity invariant are found. Some scenarios for different Gaussian bipartite states are presented and discussed.