Outcome Independence of Entanglement in One-Way Computation

TL;DR

This paper demonstrates that in one-way quantum computation, all intermediate states have identical entanglement levels regardless of measurement outcomes, highlighting a fundamental uniformity in the process.

Contribution

It proves that intermediate states in one-way computation are equivalent up to local unitaries, establishing the invariance of entanglement during the process.

Findings

Intermediate states are equivalent modulo local unitaries.

All intermediate states share the same entanglement.

The process is essentially unique with respect to local operations.

Abstract

We show that the various intermediate states appearing in the process of one-way computation at a given step of measurement are all equivalent modulo local unitary transformations. This implies, in particular, that all those intermediate states share the same entanglement irrespective of the measurement outcomes, indicating that the process of one-way computation is essentially unique with respect to local quantum operations.