Quantum Measurement (4): PBR Theorem (again)

Sorry to be repetitive, but I was just preparing this entry as John Manchak uploaded the previous post… But I still go ahead as I would like to add a few details.

The arXiv preprint by second year graduate student Matthew F Pusey of the Controlled Quantum Dynamics group at Imperial College London and his supervisors Jonathan Barrett at Royal Halloway and Terry Rudolph also at Imperial offers a potentially groundbreaking result: on just rather mild assumptions, it must be the case that the quantum state is a real physical property of a quantum system. The paper is currently under review (for Nature, it seems), but Eugenie Samuel Reich has already collected a few quotes from leading quantum foundationalists on the online portal of Nature. And, as John also mentioned below, Matt Leifer offers a very accessible account of the result on his blog.

Let me state the three assumptions that go into the theorem. The first demands that if a quantum system is prepared in a pure state, then it subsequently exemplifies a set of well-defined physical properties. Importantly, it is not assumed that the quantum state is uniquely determined by these properties. Either it is–in which case the quantum state is a physical property of the system–or it isn’t, as the ‘statistical view’ claims, according to which the quantum state “merely encodes an experimenter’s information about the properties of a system” (Pusey et al, 1).

The second premise of the theorem assumes that it is possible to prepare quantum systems independently, such that their properties are not correlated. Finally, the third stipulates that measurement outcomes solely depend on the physical properties of the different independently prepared systems (and of the measuring devices).

Pusey et al. describe a straightforward type of experiment which shows that under these three assumptions, if the set of physical properties of the quantum systems does not uniquely determine their quantum states, predictions of quantum theory are violated. In other words, what they term the “statistical view” is inconsistent with quantum mechanics, given the three premises.

This is rich food for thought for philosophers of physics, and indeed for anyone interested in the foundations of quantum mechanics. For instance, if borne out–and the proof seems valid to me–, then if a collapse theorist accepts the three premises, she must also accept that the collapse is a real physical process, forcing her to face the unmitigated mystery of non-locality in EPR-Bohm experiments.

Pusey et al. also seem to think that their result makes the many-worlds interpretation less palatable, as “it is hard to accept the conclusion that each macroscopically different component [of the quantum state] has a direct counterpart in reality.” (ibid., 4) They find this interpretation “unproblematic” (ibid.) on the statistical view. I can’t help, however, to see no (new) difficulty here for the Everettian. After all, the defenders of the many-worlds interpretation I know are all unabashed realists and will find the PBR theorem as vindication of their view.

In conclusion, the PBR theorem seems to put pressure on any interpretation of quantum mechanics which is not either thoroughly realist (and happily endorses the consequent of the theorem) or strictly instrumentalist (and denies the antecedent). It seems as if one can’t have a half-way house in the foundations of quantum mechanics.

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