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The question of which and how a particular class of entangled resource states(known as graph states) can be used for measurement based quantum computation(MBQC) recently gave rise to the notion of Flow and its generalisation gFlow.That is a causal structure for measurements guaranteeing deterministiccomputation. Furthermore, gFlow has proven itself to be a powerful tool instudying the difference between the measurement-based and circuit models forquantum computing, as well as analysing cryptographic protocols. On the otherhand, entanglement is known to play a crucial role in MBQC. In this paper wefirst show how gFlow can be used to directly give a bound on the classicalsimulation of an MBQC. Our method offers an interpretation of the gFlow asshowing how information flows through a computation, giving rise to aninformation light cone. We then establish a link between entanglement and theexistence of gFlow for a graph state. We show that the gFlow can be used tobound the entanglement width and what we call the \emph{structuralentanglement} of a graph state. In turn this gives another method relating thegFlow to bounds on how efficiently a computation can be simulated classically.These two methods of getting bounds on the difficulty of classical simulationare different and complementary and several known results follow. In particularknown relations between the MBQC and the circuit model allow these results tobe translated across models.

Entanglement, Flow and Classical Simulatability in Measurement Based Quantum Computation