Can a Third Particle Be Entangled with Two Existing Particles Without Breaking Their Entanglement?

I start with 2 entangled particles A and B. How can I entangle them with a third particle C without loosing the entanglement between A and B. Is there an example of an experiment?

wnvl2 said:

I start with 2 entangled particles A and B. How can I entangle them with a third particle C without loosing the entanglement between A and B. Is there an example of an experiment?

Yes and no

Assuming A and B are maximally entangled initially: they cannot remain maximally entangled AND also become entangled with C. That is because of something called Monogamy of Entanglement.

However you can bring C into an entangled state with A and B. I will post an experimental reference in a bit.

Here’s one to start. The technique is to create 2 maximally entangled pairs (2 photon Bell states), then create 4-fold entanglement, then drop that down to a 3 particle GHZ entangled state. It’s complicated!

The GHZ state has some parallel to the Bell state as you will see in the paper. If you measure any one to be H>, the other two will also be H>. However, the 3 have different relationships at other angles than would be evident with Bell States.

This is a proposed experiment.
https://arxiv.org/pdf/1204.0438.pdf

This is an actual experiment. This produces 6 entangled photons and drops to 3.
https://arxiv.org/pdf/2308.05709.pdf

I have plenty of other references up this line too…

Complex experiments.

What happens if my entangled particles A and B decohere a little bit with the environment? Is that an easy wat to end up with an entanglement between A, B and the environment?
Or is decoherence something absolute - all or nothing - and do I loose in that case the entanglement between A and B?

I'd indeed say that two maximally entangled particles A and B loose part of their mutual entanglement if decoherence with the environment kicks in. Decoherence is not absolute; it's e.g. only after some characteristic time scale that the density matrix of a system can be regarded as a classical probability distribution due to decoherence.

At least, as I understand it, but I'm no expert by far.

wnvl2 said:

Complex experiments.

What happens if my entangled particles A and B decohere a little bit with the environment? Is that an easy wat to end up with an entanglement between A, B and the environment?
Or is decoherence something absolute - all or nothing - and do I loose in that case the entanglement between A and B?

Do you understand what the terms entanglement and decoherence mean? It would interesting to see what definition you are using.

haushofer said:

I'd indeed say that two maximally entangled particles A and B loose part of their mutual entanglement if decoherence with the environment kicks in. Decoherence is not absolute; it's e.g. only after some characteristic time scale that the density matrix of a system can be regarded as a classical probability distribution due to decoherence.

Decoherence during the execution of an entanglement experiment - prior to arrival at the measurement apparatus - can occur. And it does not need to be all or nothing. Further, there is no specific (measurable) difference in environmental loss in setups of 3 particles vs. 2 particles.

Obviously, when you have entangled photons traveling through the open atmosphere, you get more environmental decoherence than when they are traveling by way of fiber. You can get an idea of this by looking at the reported visibility or fidelity in these experiments.

Ground-to-satellite quantum teleportation (2017)
Fidelity 80%, 1400 km through the atmosphere

Violation of Bell inequalities by photons more than 10 km apart (1998)
Visibility near 100% through fiber
"Since the visibility of the correlation function after subtracting the accidentals is close to 1, one has to conclude that the distance does not affect the nonlocal aspect of quantum mechanics, at least for distances up to 10 km."

These experimental results are not directly comparable, but you get the idea. Traveling through fiber: there is very little loss to the environment, and there is no specific time you would expect decoherence to a classical state.

PeroK said:

Do you understand what the terms entanglement and decoherence mean? It would interesting to see what definition you are using.

Quantum entanglement is the phenomenon that that the quantum state of each particle of the group cannot be described independently of the state of the others. The joint wave function cannot be factored into individual wave functions. The density operator contains off- diagonal elements.

Decoherence means that the phase relation beween A and B disappears. This implies that the off-diagonal elements of the density matrix decay. This can be explaine by entanglement with the environment.

My reasoning was that if you consider after a partial decoherence, the system of the environment C and the entangled pair A and B that we have some kind of entanglement between A, B and C.

But I assume something is going wrong here...

I think it would be more difficult to entangle a 3rd particle with two entangled particles and also completely break the entanglement between the initial two particles. At least if there is no large number of other particles present in the interaction that you do this with.

hilbert2 said:

I think it would be more difficult to entangle a 3rd particle with two entangled particles and also completely break the entanglement between the initial two particles. At least if there is no large number of other particles present in the interaction that you do this with.

Every time a molecule forms, for example, the entangled electrons in each atom combine to form a larger set of entangled electrons within the molecule.

That's the problem with viewing entanglement as some obscure phenomenon, when in fact entanglement is ubiquitous.

Yes, if you initially have two noninteracting hydrogen atoms, neither electron is likely to be at a large distance from the proton it orbits, so there is entanglement within each atom (but not necessarily in the spin variables that the concept of entanglement is usually demonstrated with). After forming an H₂ molecule, no pair of two particles within that is likely to have a large interparticle distance.