Two Groups of Entangled Photons

[StevieTNZ]

If we have two groups of photons; each group consisting of two entangled photons. We allow one of the photons from each group to interact with another object.

If we perform a polarisation measurement on each photon of one group, will the photons in the other group, independent of whether they've reached a polariser, take on a definite polarisation?

 

[lugita15]

Are you envisioning a situation in whicv you have two groups of photons, where the first photon of the first group is entangled with the first photon of the second group, and the second photon of the first group is entangled with the second photon of the second group? If so, I don't know why you have two entangled pairs of photons instead of one. But in any case, the general principle is that if photon A and photon B are entangled, then sending photon A through a polarizing filter puts photon B in a state of definite polarization, regardless of whether you ever put photon B through a polarizing filter. Does that answer your question?

 

[StevieTNZ]

Sorta. But instead one photon from each group would be entangled with an object (would that result in indirect entanglement with the other photon?) One photon from each group wouldn't be entangled directly, but would they through interacting with the same object? The 2nd photon of each group will be left as they are (no interacting with anything else).

 

[lugita15]

Sorta. But instead one photon from each group would be entangled with an object (would that result in indirect entanglement with the other photon?) One photon from each group wouldn't be entangled directly, but would they through interacting with the same object? The 2nd photon of each group will be left as they are (no interacting with anything else).

This may help: if objects A and B are entangled with respect to a certain attribute, and objects B and C are entangled with respect to the same attribute, then objects A, B, and C are all entangled with respect to that attribute.

 

[StevieTNZ]

Getting there - what I have in mind is creating two pairs of photons A + B and C + D.

Say B and C interact with another quantum object. Now if we measure photon A along a certain polarisation, B also takes on a definite polarisaton. In this scenerio, would C and D take on polarisations too?

 

[lugita15]

Getting there - what I have in mind is creating two pairs of photons A + B and C + D.

Say B and C interact with another quantum object. Now if we measure photon A along a certain polarisation, B also takes on a definite polarisaton. In this scenerio, would C and D take on polarisations too?

I'm still not clear on what your scenario is. Tell me exactly which particles are entangled with which particles, and with respect to what attribute. Since B acquires a definite polarization as soon as we do a polarization measurement on A, I'm assuming A and B are entangled with respect to polarization. And since B,C, and another quantum objects are "interacting" in some way, I assume you want B, C, and the object to be entangled, but I'm not sure with respect to what attribute. And I have no idea how D is connected with anything.

By the way, it might be useful to know that just because two particles interact does NOT imply that they become entangled. Entanglement refers to a very specific situation, where the quantum state of a two-particle (or more) system cannot be decomposed into a product of quantum states for the two separate particles. In other words, entanglement occurs when you cannot consider a two-particle system to be made of two separate one-particle systems. It is quite possible that two particles may interact in such a way that their combined quantum state CAN be decomposed so that we can view the states of the two particles completely separately. Entanglement seems to be a relatively rare phenomenon in nature.

 

[StevieTNZ]

I'm still not clear on what your scenario is. Tell me exactly which particles are entangled with which particles, and with respect to what attribute. Since B acquires a definite polarization as soon as we do a polarization measurement on A, I'm assuming A and B are entangled with respect to polarization. And since B,C, and another quantum objects are "interacting" in some way, I assume you want B, C, and the object to be entangled, but I'm not sure with respect to what attribute. And I have no idea how D is connected with anything.

Photons A and B are entangled. Photons C and D are entangled. Photons A and C 'interact' with another quantum object (E). By interact, I mean when photon A interacts with the polariser. I'm using the term entanglement loosely by meaning when there is an interaction like a measurement. Of course that is not the only interaction that can occur.

Photons A and C don't interact directly. In regards to the quantum object A and C do encounter, it is not as a measurement of polarisation. It could simply hit it, producing a result, or whatnot. Without getting too lost into details over it, it would seem A interacted with E, as well as C interact with E. I measure the polarisation of B and A takes on a definite polarisation. At that time, because C interacted with E, do C and D take on polarisations?

 

[lugita15]

Photons A and B are entangled. Photons C and D are entangled. Photons A and C 'interact' with another quantum object (E). By interact, I mean when photon A interacts with the polariser. I'm using the term entanglement loosely by meaning when there is an interaction like a measurement. Of course that is not the only interaction that can occur.

Photons A and C don't interact directly. In regards to the quantum object A and C do encounter, it is not as a measurement of polarisation. It could simply hit it, producing a result, or whatnot. Without getting too lost into details over it, it would seem A interacted with E, as well as C interact with E. I measure the polarisation of B and A takes on a definite polarisation. At that time, because C interacted with E, do C and D take on polarisations?

No; since neither C nor D is entangled with particles A and B, there is no reason why a polarization measurement of A or B should make C or D have a definite polarization. This situation may of course be different if the interaction between A, C, and the mysterious object actually does result in some kind of entangled quantum state with respect to polarization.

 

[StevieTNZ]

No; since neither C nor D is entangled with particles A and B, there is no reason why a polarization measurement of A or B should make C or D have a definite polarization. This situation may of course be different if the interaction between A, C, and the mysterious object actually does result in some kind of entangled quantum state with respect to polarization.

Ah okay. Thanks for that. If A and C did get entangled with the object in regards to polarisation, it wouldn't necessarily mean measurement of polarisation at the time (i.e. it interacts with the object, then gets measured later on)?

 

[lugita15]

Ah okay. Thanks for that. If A and C did get entangled with the object in regards to polarisation, it wouldn't necessarily mean measurement of polarisation at the time (i.e. it interacts with the object, then gets measured later on)?

You can have three (or any number of) objects getting in an entangled state without any measurement taking place.

But of course the whole question of measurement leads into hairy questions of interpretation. It's more of a philosophical question to decide at what stage the wave function collapses, if at all. The closest thing to a consensus view on the subject among practical people (who tend to shy away from philosophy) is decoherence, which means that once you have a lot of particles in your system quantum interference and superposition effects become hard to detect. But of course you also have consciousness-causes-collapse, Bohmian, and many others.

 

[StevieTNZ]

I've always wondered about this: if we have a photon that has available two choices (in superposition of two states) going along two paths, that lead to two different objects (say two polarisers), does QM predict the quantum object gets entangled with both of those polarisers (as Schrödinger's equation evolves as a superposition of both paths)?

 

[lugita15]

I've always wondered about this: if we have a photon that has available two choices (in superposition of two states) going along two paths, that lead to two different objects (say two polarisers), does QM predict the quantum object gets entangled with both of those polarisers (as Schrödinger's equation evolves as a superposition of both paths)?

There are two ways to think about this. You can think of the polarizer as performing a measurement of the photon, and thus the the wave function of the photon collapsing. Or you can think of the photon-and-polarizer system, and the wave function of this combined system does not collapse when the photon and polarizer interact; it may change, but it will just keep evolving. Which approach to take is an interpretational question, because a famous theorem of von Neumann states that you can't experimentally tell the difference: regardless of which approach you take, you'll end up making the exact same predictions about the photon's behavior in any experiment. That's because you can't tell whether the photon's state collapsed when you made a measurement of it, or whether it had already collapsed when it interacted with the polarizer.