Measurement based quantum communication with resource states generated by entanglement purification

TL;DR

This paper explores measurement-based quantum communication using noisy resource states from entanglement purification, showing advantages over traditional methods and linking high fault-tolerance thresholds to gate-based models.

Contribution

It demonstrates that resource states generated by entanglement purification enable effective measurement-based quantum communication with noise models that are well-approximated by local errors.

Findings

Local error model accurately describes noise in resource states

Measurement-based approach outperforms direct transmission and gate-based error correction

High fault-tolerance thresholds are linked to local error models in resource states

Abstract

We investigate measurement-based quantum communication with noisy resource states that are generated by entanglement purification. We consider the transmission of encoded information via noisy quantum channels using a measurement-based implementation of encoding, error correction and decoding. We show that such an approach offers advantages over direct transmission, gate-based error correction and measurement-based schemes with direct generation of resource states. We analyze the noise structure of resource states generated by entanglement purification and show that a local error model, i.e. noise acting independently on all qubits of the resource state, is a good approximation in general, and provides an exact description for $GHZ$-states. The latter are resources for a measurement-based implementation of error correction codes for bit-flip or phase flip errors. This provides a first link between the recently found very high thresholds for fault-tolerant measurement-based quantum information processing based on local error models for resource states, to error thresholds for gate based computational models.