The cost of quantum locality

It has been more than 20 years since Deutsch and Hayden demonstrated that quantum systems can be completely described locally—notwithstanding Bell’s theorem. More recently, Raymond-Robichaud proposed two other approaches to the same conclusion. In this paper, all these means of describing quantum systems locally are proved formally equivalent. The cost of such descriptions is then quantified by the dimensionality of their underlining space. The number of degrees of freedom of a single qubit’s local description is shown to grow exponentially with the total number of qubits considered as a global system. This apparently unreasonable cost to describe such a small system in a large Universe is nonetheless shown to be expected. Finally, structures that supplement the universal wave function are investigated.

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.