Alternative Experimental Protocol for a PBR-Like Result

Pusey, Barrett and Rudolph (PBR) [1] have proven a new theorem which imposes a significant constraint on the interpretation of quantum mechanics [2]. The theorem shows that if one assumes that quantum systems possess physical states λ which are solely responsible for determining the outcomes of experiments performed on the quantum systems, then no two distinct quantum states |u〉 and |v〉 can share the same physical state λ. It follows that any quantum state |u〉 is uniquely co-ordinated with a subset of the λ and therefore should itself be regarded as a physical property of the quantum system. In the terms of Ref. [3], models of quantum mechanics that assume there are physical states are classified as ψ-epistemic if there are two states which share the same physical state λ and as ψ-ontic if there is no pair of states which share the same λ. Thus PBR show that all such models of quantum mechanics are ψ-ontic. Hall has shown that the assumptions used in the PBR theorem can be weakened and so the theorem can be generalised [4]. Colbeck and Renner [5] have reached the same conclusion as PBR via a different route and furthermore concluded that the quantum state is the only physical property of the quantum system. The experimental protocol for the PBR theorem [1] requires a minimum of N = 2 sources of the two arbitrary states |u〉 and |v〉 that are involved. When |〈u|v〉| > 1/2, N > 2 sources are required and as |〈u|v〉| → 1, N →∞. As N becomes larger, the experimental error that can be tolerated becomes smaller [1]. As well as gates which operate on the individual states, the protocol requires an N -bit entangling gate operating without post-selection. It is interesting to investigate alternative experimental protocols to implement the PBR strategy for three reasons. Firstly, alternative protocols may be easier to implement experimentally. Secondly, the PBR result is a very strong result because it applies to any two quantum states. Proving the result for any two quantum states is necessary to deal with the formal definition of ψ-epistemic [3] (see above). However a ψ-epistemic model which literally had just two states which share the