Vindication of quantum locality

In a previous paper, Hayden and I (Deutsch & Hayden 2000 Proc. R. Soc. Lond. A 456, 1759-1774. (doi:10.1098/rspa.2000.0585)) proved, using the Heisenberg picture, that quantum physics satisfies Einstein's criterion of locality. Wallace and Timpson (Wallace & Timpson 2007 Found. Phys. 37, 951-955. (doi:10.1007/s10701-007-9135-7)) have argued that certain transformations of the Heisenberg-picture description of a quantum system must be regarded as leaving invariant the factual situation being described, and that taking this into account reveals that Einstein's criterion is violated after all. Here, I vindicate the proof and explain some misconceptions that have led to this and other criticisms of it.