How do you tell when particles are or aren't entangled?

[louthinator]

TL;DR Summary

How is it that you can tell the difference between a set of entangled and non-entangled particles and how can you tell when particles become no longer entangled?

Do changes of any kind happen in an entangled system?

I'm trying to get my head around the principles of quantum entanglement (would love to get some schooling on the issue but I don't have that kind of money) and trying to discern the actual science from the horrible misconceptions is difficult. I know you can't transmit information faster than light so entanglement can't be used for that, but there is something I've been curious about, and that's if entanglement was broken would that then cause some kind of change in the once-entangled particles? how quickly could that be known if it occured? when the particles go from being not individuals but 2 halves of a whole to being complete unto themselves again.

 

[Drakkith]

As far as I understand, there's no way to tell that a particle is entangled with a partner particle except by knowing its previous creation/interaction event. For example, if you detect a photon, you have no way of knowing whether it was entangled with another photon unless you know in advance that it was part of an entanglement experiment (or whatever phenomenon entangled it).

when the particles go from being not individuals but 2 halves of a whole to being complete unto themselves again.

There is no 'fingerprint' on a particle that would let you know it was or is entangled. If you detect a photon, all you know is that you've detected a photon, not whether that photon is entangled.

 

[louthinator]

As far as I understand, there's no way to tell that a particle is entangled with a partner particle except by knowing its previous creation/interaction event. For example, if you detect a photon, you have no way of knowing whether it was entangled with another photon unless you know in advance that it was part of an entanglement experiment (or whatever phenomenon entangled it).There is no 'fingerprint' on a particle that would let you know it was or is entangled. If you detect a photon, all you know is that you've detected a photon, not whether that photon is entangled.

so what's all the hype surrounding entangled particles and quantum computing? do entangled particles have any uses at all or is it just a case of "we know it exists"

 

[PeterDonis]

How is it that you can tell the difference between a set of entangled and non-entangled particles

For a single pair of particles, you can't.

But if you have some source of pairs of particles, that is supposed to produce each pair in the same state, you can do experiments on the pairs and analyze the statistics of the results to determine if the state being produced by the source is an entangled state. A term to search on would be "quantum state tomography" to find out more about how this works.

 

[PeroK]

so what's all the hype surrounding entangled particles and quantum computing? do entangled particles have any uses at all or is it just a case of "we know it exists"

Quantum computing relies on being able to create and maintain a system of entangled particles.

 

[Kolmo]

Basic procedure of learning the state:
So to investigate entanglement between a set of $N$ particles, as mentioned above you would perform measurements on sequences of such $N$-groups and looking at the results one would slowly build up enough statistics to infer the state of the $N$-group as a whole. This is known as state tomography.

There are forms of $N$-particle entanglement that are not just sums of pair entanglement, just something to note. So you can have three particles which are entangled in such a way that each pair may not appear entangled if you only accessed that pair.

Difficulties with the basic procedure:
When you are performing state tomography I just said you perform "sequences of measurements", however a big part of state tomography is actually choosing the right measurements that allow you to learn the state as quickly as possible. The most efficient measurements in an information theoretic sense are called MIC-POVMs, but it might not be easy to build a MIC-POVM measurement device for the quantum system you are investigating. So there's a whole area about figuring out which device gets as close to a "very informative" measurement like a MIC-POVM while still being something you can actually build in a lab.

Also note that when you build a new device there can be a bit of ambiguity as to what measurement it is performing. So you have to do a type of device tomography on new devices themselves to learn what measurement they are performing.

How much entanglement:
Once all this is done and you have learned the state, you can now apply what is called an entanglement measure to the state. This is a function of the state that is zero if the state is separable/not-entangled and increases the "more entangled" the state is. Unfortunately the measures don't all have the same values or even order states the same way, i.e. for two states they might disagree on which one is more entangled. Also when you add relativity into the picture (to get quantum field theory) some of the measures have severe issues like diverging/blowing up to infinity.

 

[Strilanc]

To make things simple, you'll want to know which entangled state you're checking for. For example, maybe the relevant entangled state is $|00\rangle + |11\rangle$. The stabilizer generators of that state are $X_1 X_2$ and $Z_1 Z_2$. No other state has those generators. Therefore we can check for the state by measuring the X-parity and Z-parity of the two qubits and seeing that they are both +1.

This check is probabilistic. It will always succeed for the state $|00\rangle + |11\rangle$, but for other states it will only probabilistically fail. For any separable state the check will reject them 50% of the time.

This check is destructive. If you started with a separable state, performing this check on it will actually force the involved qubits to become entangled.

Both these issues are unavoidable (e.g. if you could avoid them you would violate the no cloning theorem). As a result, these checks would usually be used for figuring out what is being produced by a repeatable process for producing a state, instead of figuring out an individual state.

 

[f95toli]

so what's all the hype surrounding entangled particles and quantum computing? do entangled particles have any uses at all or is it just a case of "we know it exists"

Although you can do quantum computing using photons, most platforms use systems which are much easier to understand in that you don't need to destroy them to measure them. Superconducting qubits are relatively large (sometimes up to a 1mm) electronic circuits on a chip and ion trap qubits are ions that are more or less permanently held in a trap (they can stay there for days) which you can literally "see" using a camera,

You can entangle two superconducting qubits by connecting them via a capacitor and then applying the right combination of microwave pulses. There are then many ways to check if the two qubits actually ended up entangled, Strilanc and Kolmo have already outlines some methods. I'd say full state tomography is the most "stringent" method for doing this.

 

[DrChinese]

so what's all the hype surrounding entangled particles and quantum computing? do entangled particles have any uses at all or is it just a case of "we know it exists"

The objective is to prove better and better descriptions of the physical world. They don't need specific "uses", although uses are often found later. Entangled systems are predicted by QM, and those predictions have been supported experimentally. The "hype" is that entangled systems have spatio-temporal extent that violate classical norms of locality. I.e. distance is not a limiting factor.

It is interesting to note that there is no observable difference in outcomes when considering the order of measurements on components of an entangled system. Did Alice or Bob measure first? This does not seem to change anything, and it is not possible to point to one or the other as causing a "collapse" (this word is loaded with baggage in QM) of the wavefunction.