Is a bipartite system necessary for the proof of the PBR theorem?

[greypilgrim]

Hi.

I'm trying to grasp what the PBR theorem is about. I'm not tackling the full version, but rather the simple example in @Demystifier's summary.

While I think I understand the mathematical steps, my question is why you need two systems to prove it. Is this only technical or more fundamental?

I mean it's not that surprising for a no-go theorem to make use of a bipartite system, but the crucial thing about that, such as in Bell's theorem, usually is that those systems are entangled. Here they just seem to be in a product state.

 

[Demystifier]

my question is why you need two systems to prove it. Is this only technical or more fundamental?

It's not clear. Hardy found a different proof without assuming two systems, but he used an additional technical assumption the physical meaning of which is not entirely clear.

 

[QLogic]

I mean it's not that surprising for a no-go theorem to make use of a bipartite system, but the crucial thing about that, such as in Bell's theorem, usually is that those systems are entangled. Here they just seem to be in a product state

The measurements used for the contradiction are in the Bell basis though.