Characterising port-based teleportation as a universal simulator of qubit channels

TL;DR

This paper characterizes port-based teleportation as a universal method for simulating various qubit channels, providing explicit descriptions and improving simulation accuracy for specific channels like amplitude damping.

Contribution

It offers a complete characterization of the Choi matrix of channels simulated by PBT with general resource states, advancing understanding of PBT's capabilities.

Findings

Explicit formula for the Choi matrix of simulated channels

Description of the resource-to-channel map in PBT

Enhanced simulation of amplitude damping channel

Abstract

Port-based teleportation (PBT) is a teleportation protocol that employs a number of Bell pairs and a joint measurement to enact an approximate input-output identity channel. Replacing the Bell pairs with a different multi-qubit resource state changes the enacted channel and allows the PBT protocol to simulate qubit channels beyond the identity. The channel resulting from PBT using a general resource state is consequently of interest. In this work, we fully characterise the Choi matrix of the qubit channel simulated by the PBT protocol in terms of its resource state. We also characterise the PBT protocol itself, by finding a description of the map from the resource state to the Choi matrix of the channel that is simulated by using that resource state. Finally, we exploit our expressions to show improved simulations of the amplitude damping channel by means of PBT with a finite number of ports.