# A question about relations between twistor, entanglement and light ray

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?

• Is the association between twistor and 2-qubit state, your invention? – Mitchell Porter May 16 '17 at 9:52
• I did not see it before. Also I never claim that I invent it. I just show my own observation during my reading. I only know there are some work to understand 3 qubits by twistor theory. Do you have any reference/paper about this? I am just tying to understand related topics. @ Mitchell Porter – XXDD May 16 '17 at 15:19
• I do not get you. Are you saying that there is already a clear picture about it or you are questioning this observation? I know my way to associate a twistor and a 2 qubit system may be wrong since I think it's a little ridiculous. That's why I ask the question, I want to find out what's wrong with my understanding@Mitchell Porte – XXDD May 16 '17 at 15:25
• I wanted to know if you were referring to a big picture that I didn't know about. These are simple mathematical objects so there are many relationships... Anyway, I will attempt an answer. – Mitchell Porter May 16 '17 at 20:32
• I am just trying to understand the light ray from an information processing point of view. Light rays are so special in both physics and information processing, so I am trying to find out what's its correspondence in information processing system. I can associate it with a separable 2 qubit state (both pure or mixed), but the twistor theory shows a different picture with my understanding. So I am confused.@ Mitchell Porter – XXDD May 17 '17 at 3:03

Einstein said, make it simple, but not too simple... It is like if someone learns about prime numbers, and they see that most of them are odd, but one of them is even. Is it a contradiction? No, it just means that the facts about numbers are more complicated than "all prime numbers are odd" or "all even numbers are composite".

In this case, we are talking about something like "physical applications of complex-number geometries". The twistor space can describe a light ray, the twistor space can also describe two qubits, but the relationship to entanglement is somehow different in spirit in the two applications.

Well, that's not a logical contradiction. It just means there is a bigger context. I don't know what it is.

Maybe you make a twistor by entangling two spinors, and then you make space-time by entangling twistors. If that's the answer, then the resolution of your paradox is that from a space-time perspective, a twistor is elementary, but from a "pre-space-time" perspective, a twistor is composite.

• Thanks. In fact I am fascinated by the role of light ray in information processing. Light rays are the fastest route to transfer information, or to change the state of a qubit. The spooky action of entanglement can also be regarded as a 'superluminal' way to change a state of a qubit. So I am thinking that entanglement (superluminal) should be different with the light ray. I think that a twistor should not be connected with a pair of entangled qubits and my way to associate entanglement with a twistor is wrong. But I do not know how to fix it. – XXDD May 19 '17 at 8:16