  Measurement-based quantum computing (MBQC) is a universal model for quantum
computation. The combinatorial characterisation of determinism in this model,
powered by measurements, and hence, fundamentally probabilistic, is the
cornerstone of most of the breakthrough results in this field. The most general
known sufficient condition for a deterministic MBQC to be driven is that the
underlying graph of the computation has a particular kind of flow called Pauli
flow. The necessity of the Pauli flow was an open question. We show that the
Pauli flow is necessary for real-MBQC, and not in general providing
counterexamples for (complex) MBQC. We explore the consequences of this result
for real MBQC and its applications. Real MBQC and more generally real quantum
computing is known to be universal for quantum computing. Real MBQC has been
used for interactive proofs by McKague. The two-prover case corresponds to
real-MBQC on bipartite graphs. While (complex) MBQC on bipartite graphs are
universal, the universality of real MBQC on bipartite graphs was an open
question. We show that real bipartite MBQC is not universal proving that all
measurements of real bipartite MBQC can be parallelised leading to constant
depth computations. As a consequence, McKague techniques cannot lead to
two-prover interactive proofs.
