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

In summary, the discussion is about the PBR theorem and its simple example. The question is why two systems are needed to prove it and whether this is just a technical requirement or has a deeper meaning. It is noted that Hardy found a different proof without assuming two systems, but with an unclear physical assumption. The use of bipartite systems in no-go theorems is also mentioned, but it is pointed out that in this case the systems are in a product state. The measurements used for the contradiction are noted to be in the Bell basis.
  • #1
greypilgrim
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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.
 
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  • #2
greypilgrim said:
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.
 
  • #3
greypilgrim said:
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.
 

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

1. What is the PBR theorem?

The PBR (Pusey-Barrett-Rudolph) theorem is a result in quantum mechanics that states that if a physical theory is to reproduce the predictions of quantum mechanics, it must be non-contextual (i.e. the outcome of a measurement cannot depend on the context in which it is measured) and have a bipartite (two-part) structure.

2. What is a bipartite system?

A bipartite system is a system that can be divided into two distinct parts, with each part having its own set of properties and interactions. In the context of the PBR theorem, a bipartite system refers to the division of a physical system into two distinct parts or subsystems.

3. Why is a bipartite system necessary for the proof of the PBR theorem?

The PBR theorem relies on a mathematical proof that shows that any physical theory that reproduces the predictions of quantum mechanics must have a bipartite structure. This is because a bipartite structure is a necessary condition for a theory to be both non-contextual and reproduce the predictions of quantum mechanics.

4. Can the PBR theorem be proven without a bipartite system?

No, the PBR theorem cannot be proven without a bipartite system. As mentioned earlier, a bipartite structure is a necessary condition for the proof of the PBR theorem. Without it, the theorem would not hold.

5. Are there any real-world applications of the PBR theorem?

While the PBR theorem is primarily a theoretical result, it has implications for our understanding of quantum mechanics and the nature of reality. It also has potential applications in the field of quantum information and communication, as it helps us better understand the limitations and possibilities of quantum systems.

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