Consider the unitary circuit model of quantum computation. If we need to generate entanglement between the input qubits with the circuit, it must have multi-qubit gates such as CNOT, as entanglement cannot increase under local operations and classical communication. Consequently, we can say that quantum computing with multi-qubit gates is inherently different from quantum computing with just local gates. But what about measurements?
Does including simultaneous measurements of multiple qubits make a difference in quantum computing or can we perhaps emulate this with local measurements with some overhead? EDIT: by "emulate with local measurements", I mean have the same effect with local measurements + any unitary gates.
Please notice that I am not merely asking how measuring one qubit changes the others, which has already been asked and answered, or if such measurements are possible. I am interested to know whether including such measurements could bring something new to the table.