Universality of Computation in Real Quantum Theory

TL;DR

This paper demonstrates that the C-NOT gate, combined with local gates, is universal for Realtime Quantum Theory, highlighting differences from complex quantum theory and emphasizing the importance of local discriminability and qubit structure.

Contribution

It proves the universality of C-NOT in Real Quantum Theory, contrasting with complex quantum theory, and clarifies the role of local discriminability and qubit structure.

Findings

C-NOT is universal for RQT with local gates

Extra rebit needed for reversible computation in RQT

Short proof of C-NOT universality in CQT

Abstract

Recently de La Torre et al. [1] reconstructed Quantum Theory from its local structure on the basis of local discriminability and the existence of a one-parameter group of bipartite transformations containing an entangling gate. This result relies on universality of an entangling gate for quantum computation. Here we prove universality of C-NOT with local gates for Real Quantum Theory (RQT), showing that such universality would not be sufficient for the result, whereas local discriminability and the qubit structure play a crucial role. For reversible computation, generally an extra rebit is needed for RQT. As a byproduct we also provide a short proof of universality of C-NOT for CQT.