In his book 'The road to reality', R. Penrose wrote:
It is possible to regard twistor theory as a continuation of the spin network programme to obtain a relativistic scheme, in which idealized light rays (or their generalizations, with spin) appear to be, in a sense, the carriers of quanglement. Ordinary spacetime notions are not initially among the ingredients of twistor theory but are to be constructed from them. This has a good deal in common with the underlying philosophy behind my original spin networks, where spatial notions are to be constructed from the spin networks, rather than the spin networks being thought of as inhabiting a previously assigned spatial geometry.
My understanding of his words is that:
If a twistor is a light ray, and a light ray is a way to carry quantum entanglement, then a twistor is closely related with quantum entanglement. Of course we can easily associate a twistor $z=[z_0,z_1,z_2,z_3]$ (4 complex numbers) with a 2 qubit state $|\psi>=z_0|00>+z_1|01>+z_2|10>+z_3|11>$ by just normalizing $z$.
Yes, the above mapping between a twistor and a 2 qubit state does show something interesting, since it can be easily verified that a separable pure state can not correspond to a null twistor and only entangled states (with respect to a local unitary transformation) might correspond to null twistors.
But the problem is that, the above picture seems to say: any entangled 2 qubit state corresponds to a light ray, no matter how strong the entanglement is. For me this is not satisfactory since states with different entanglements should not all corresponds to light rays since all light rays are equivalent but states with different entanglements are not.
From another point of view, light rays are supposed to separate causal/noncausal events in spacetime. If the slogan 'entanglement is the glue of spacetime' is true, then it's natural to regard light rays as the boundary between entangled and non-entangled states since this means that 'beyond the light ray, spacetime/causality is broken'. For me, causality seems to stand for 'events strongly connected by spacetime glue/entanglement'.
Another fact is that the (1/2,1/2) spinor representation of Lorentz group and the formation of entanglement of 2 qubit states also show some signs of relating separable states with light rays.
So I have two different conclusions: twistor connects light rays with both strong and weak entanglement, quantum information theory connects light rays with the boundary between entangled/separable states.
My question is:
Is a light ray something to carry entanglement as Penrose said, or it's something to separate entangled/nonentangled states? Or if light rays stand for 'strong/sticky glue/entanglement carrier', then what stands for the 'very weak glue carrier'? Or light rays can be both strong and weak glue?
Or I am confused by the question: Is a light ray something to deliver the strongest correlation/causality/entanglement or to deliver the weakest correlation/causality/entanglement?