B How do particles become entangled?

[ISamson]

Hi.
I know that particles can become entangled, but I don't understand the actual physical process that the particles are involved into become entangled. Can anyone help me?
Thanks.

 

[jtbell]

While you're waiting for an answer, check out the "Similar discussions" listed at the bottom of this page.

(At least, they're there if you're using a web browser. I don't know if they're in the PF phone app.)

 

[Lord Jestocost]

Hi.
I know that particles can become entangled, but I don't understand the actual physical process that the particles are involved into become entangled. Can anyone help me?
Thanks.

Maybe, this entry from Chad Orzel's blog might be of interest for you: https://www.forbes.com/sites/chador...you-create-quantum-entanglement/#5432496d1732

 

[Simon Phoenix]

I know that particles can become entangled, but I don't understand the actual physical process that the particles are involved into become entangled. Can anyone help me?

That's quite a big question

In very general terms things become entangled when they interact - so the number of physical processes that create entanglement is quite extensive. Entanglement is not some rare and special prediction of quantum mechanics - it's pretty much par for the course. Interact two quantum objects and you'll pretty much always entangle them to some extent. It's actually hard to avoid.

OK - that's a bit simplistic and I've skirted over rather a major issue - and direct interaction isn't the only way to create entanglement. But QM predicts that if we start off 2 objects in what's called a 'pure' state and let them interact (somehow) then, unless we have a special kind of interaction, we'll entangle the 2 objects (actually we don't require the objects to be in pure states, strictly speaking, but the 'less pure' they are to begin with the less entanglement we'll be able to create through interaction).

One way to think of a pure state is that it's the most complete description of a system that we can have. The problem here is that it isn't all that easy to start off with everything in one of these pure states. In order to prepare (and keep) something in one of these pure states we have to isolate it somewhat - if it interacts with the 'environment' then we're going to lose some information about the state (think of a molecule in a gas and suppose we know everything about it at some time. A short time later it's been knocked about by the zillions of other molecules - so our molecule experiences an environment that continually changes its state and consequently we might only have 'average' information after only a short time has elapsed).

That's only a picture to get across the idea; QM predicts that interactions entangle things - the environment messes this up.

So although QM predicts that for these ideal, pure, states interactions create entanglement - actually working with these pure states to demonstrate entanglement is quite difficult because we have to keep the nasty environment from poking its messy nose in.

The answer to your question is that there isn't one specific physical 'process' that creates entanglement - there are lots of ways to create entanglement. In general, when things interact they become entangled - that's a pretty general prediction of QM.

Just to confuse things further there's a rather curious process known as 'entanglement swapping'. Let's suppose Alice has 2 perfectly entangled particles 1 and 2. And we'll suppose that Bob has another pair of entangled particles 3 and 4. Alice gives particle 2 to Clive. Bob gives particle 3 to Clive. Now Alice heads off to London and Bob dashes off to Sydney. Some time later Clive does something to particles 2 and 3 (don't worry about what that something is). Now particle 1 in London and particle 4 in Sydney are in an entangled state - particle 1 and 4 have never even been introduced, let alone held hands, so to speak.

This seems rather non-local - but it's OK because Alice and Bob can't 'do' anything with their newly entangled particles until Clive supplies some information about what he did. In essence Alice and Bob don't know which particular kind of entangled state they have until Clive tells them.

It's an interesting example because particles 1 and 4 here have never directly interacted - indeed they might never have even been on the same continent. So there's at least one way we can create entanglement without direct interaction.

 

[Leo1233783]

Searchers found that a dead particle could be entangled this way. But what are exactly the maths ?

 

[Nugatory]

Searchers found that a dead particle could be entangled this way. But what are exactly the maths ?

I'm sorry, but I'm not understanding what you mean by a "dead particle".

 

[Leo1233783]

very badly worded, sorry; in Entanglement Between Photons that have Never Coexisted , authors claim

Here we demonstrate these principles by generating and fully characterizing an entangled pair of photons that never coexisted. Using entanglement swapping between two temporally separated photon pairs we entangle one photon from the first pair with another photon from the second pair. The first photon was detected even before the other was created​

They start with 2 independant entangled pairs 1,2 and 3,4. They measure 1 and a small time later 2 and 3 and a small time later 4.

• The only relation between 2 and 3 is that they live the same event: a measure in an experiment. It is not an interaction
  
• The 2 measure devices are independant.
• In fact the 2 pairs are not independant: it is the same source alternatively used for 1,2 and 3,4, see the setup.
  
• The projection concept is not mainstream.

And then, they say :

When the two photons 2 and 3 are projected onto any Bell state, the first and last photons (1
and 4) collapse also into the same state and entanglement is swapped.​

In many discussions around this publication, some conclude that it was the measure of the 4th particle which had
setted the first by time reversal.

I do not feel comfortable with any idea of this kind. I hold myself back... There are probably another interpretations.

 

[Trollfaz]

I would say that when 2 particles interact or are formed from the same event such that both must obey certain laws such as the conservation of angular momentums.

 

[Leo1233783]

I would say that when 2 particles interact or are formed from the same event such that both must obey certain laws such as the conservation of angular momentums.

they are not formed from the same event like in an EPR experiment.
there is no interaction, just independent measurements.

Duplicate the experiment at 2 meters and start them at the same time.
Now, consider the crossed "projections" between 2 , 3 , 2 bis and 3 bis. This may bring a lot of constraints.

 

[ISamson]

Thank you everyone!
Very useful and successful explanations.

 

[Simon Phoenix]

The projection concept is not mainstream.

I don't agree with you here. In practice, the projection 'postulate' is used extensively when calculating stuff (certainly in quantum optics/information anyway). Whether one views this as representative of a physical 'collapse' or merely as a convenient mathematical tool for getting the right answers is irrelevant here.

One can avoid using this postulate if you want - personally I find the calculations harder doing it that way - I have to mangle my thoughts into a place that doesn't work so well for me.

So for the entanglement swapping the basic idea is this. Start off with (1,2) and (3,4) being entangled pairs of qubits. In principle we could have the pair (1,2) in London and pair (3,4) in New York. Now let's courier particles 2 and 3 to Manila. Clive, on holiday in the Philippines, performs a Bell measurement on the particle pair (2,3) - and we suppose it is possible to do an ideal measurement here (some people on here call it a filter measurement, I've always known this as an ideal von Neumann measurement).

Using the projection 'picture' - the state of the particles (1,4) will be projected into one of the 4 entangled Bell states after Clive's measurement/filter. Thinking that way makes the calculation really easy. Yes, I agree that we don't have to do it this way, but why make life difficult for oneself?

We could imagine having large numbers of such pairs. If Clive does the measurement on these pairs and some short time later (we'll imagine them all in the same frame of reference with synchronised clocks) Alice and Bob (who have qubits 1 and 4, respectively) now do a standard set of measurements that they would do if they were going to test for violations of Bell's inequality.

When they subsequently get the results of Clive's measurements on each particle pair (2,3) they will be able to identify 4 sub-ensembles, one for each of Clive's 4 possible results - and they will find a violation of the Bell inequality for each sub-ensemble, but no violation for the entire data set.

Whether you use the projection postulate or not when you're working out the prediction for the measurements on the sub-ensembles you'll get the same prediction - each sub-ensemble shows a violation of the BI. It's up to you how you interpret that result - for me it's just a whole lot easier to imagine that each particle in a sub-ensemble has been projected into a definite Bell state by Clive's measurement. But of course there are known 'philosophical' problems with thinking this way (you won't predict the wrong results for experiments but thinking in 'projection' terms doesn't sit too well with relativity).

Yer pays yer money and you takes yer pick

You can go nuts and use the POVM formalism to calculate the results and their probabilities for the ideal entanglement swapping case - throw the whole 'no-projection' shebang at it, but the POVM formalism contains all of the ideal filter measurements and the 'projection' as a special case anyway. The utility of the POVM formalism is that it allows us to consider non-ideal measurements in a general theoretical setting (generalized measurements) so we can consider the case of entanglement swapping if we had a non-ideal measurement, for example. Furthermore every measurement we can dream up (ideal or otherwise), can be represented as a POVM. This then allows us to optimise results over $all$ possible measurements - a useful thing to do in QKD, for example, where one might be interested in the lowest possible error rate caused by a measurement. But every POVM can also (theoretically) be represented as a system coupled to an ancilla upon which ideal 'projective' measurements are made - so I would argue that the notion of 'projection' is sort of really hiding in there anyway

So the notion of 'projection' still gets used quite a lot - even if ultimately we must consider it as just a cute mathematical device for getting to the right answers quicker (results and their probabilities and states after measurement so that we can predict results and probabilities of subsequent measurements).

 

[vanhees71]

very badly worded, sorry; in Entanglement Between Photons that have Never Coexisted , authors claim

Here we demonstrate these principles by generating and fully characterizing an entangled pair of photons that never coexisted. Using entanglement swapping between two temporally separated photon pairs we entangle one photon from the first pair with another photon from the second pair. The first photon was detected even before the other was created​

They start with 2 independant entangled pairs 1,2 and 3,4. They measure 1 and a small time later 2 and 3 and a small time later 4.

• The only relation between 2 and 3 is that they live the same event: a measure in an experiment. It is not an interaction
  
• The 2 measure devices are independant.
• In fact the 2 pairs are not independant: it is the same source alternatively used for 1,2 and 3,4, see the setup.
  
• The projection concept is not mainstream.

And then, they say :

When the two photons 2 and 3 are projected onto any Bell state, the first and last photons (1
and 4) collapse also into the same state and entanglement is swapped.​

In many discussions around this publication, some conclude that it was the measure of the 4th particle which had
setted the first by time reversal.

I do not feel comfortable with any idea of this kind. I hold myself back... There are probably another interpretations.

Why are you not comfortable with this phenomenon, called "entanglement swapping". As far as I know it has been confirmed by experiment and it's well understood from standard QT (in this case QED). Nature doesn't ask whether you like how you she behaves. Physics is simply a method to figure out, how Nature behaves.

 

[Leo1233783]

Why are you not comfortable with this phenomenon, called "entanglement swapping".

what do you think of the case where there are 2 duplicate experiments starting a the same time?

Could you please point on the QED publication claiming something about this swapping ?

 

[vanhees71]

https://en.wikipedia.org/wiki/Quantum_teleportation

 

[ISamson]

https://en.wikipedia.org/wiki/Quantum_teleportation

Yes, I've viewed a documentary on this. Cool, eh?

 

[Leo1233783]

this morning I changed my mind. You are all true. Have good feast ...

 

[sirios]

Hi.
I know that particles can become entangled, but I don't understand the actual physical process that the particles are involved into become entangled. Can anyone help me?
Thanks.

greetings, good to answer, it is necessary to know that the QM itself does not explain perfectly what "transmitted information" from one particle to another, we only know that 2 particles share their "information" as (spin, wave function and other properties ) however many articles claim that interlacing is very common. the reason why the quantum entanglement is difficult to measure and because the environment can affect the measurement as the post 4# cites, there are also more intense interlacings, that is, not only the properties intertwine but also the states, also exist other phenomena involving quantum entanglement.