[tooltower]

> How can entangled system be differentiated from a nonentangled system?

The canonical answer to your question is Bell's inequality: https://en.wikipedia.org/wiki/Bell's_theorem. But TL;DR: the distinction only shows up in the statistics of repeated experiments. There is _no way_ to distinguish them in single-fire experiments. Entanglement is defined in terms of "odd" statistics.

In repeated measurements of related properties (e.g. spin along varying angle), entangled systems show more correlation than it should be possible classically.

[guy234]

So does this imply that the phrase "entangled system" doesn't mean anything about a specific system but rather indicates which types of statistics govern a class of systems produced en mass?

[abdullahkhalids]

The Bell experiment is one test of entanglement. There is a whole class of tasks that you can do only if you have access to entangled systems. Take another one to see how the implication you state doesn't follow.

For example, quantum teleportation is only possible if you have a source that produces entangled particles. If I want to test that you have such a source, I can give you a random state (which only I know), and ask you to teleport it to a far away location [1]. If you indeed have an entangled particle source, then you can successfully teleport the state 100% of the time. However, because measurements in quantum mechanics are probabilistic, I can't actually single-shot verify that you teleported the correct state. So we will have to repeat this task many times [2], and with each success I will be more and more sure that you have an entangled state source.

Now coming to your musing above: "rather indicates which types of statistics govern a class of systems produced en mass"

You can see why this is not consistent with the repeated teleportation experiment. If every single teleportation test succeeded individually, then every iteration must have involved an entangled state. The repeat is only because of my inability to verify in single-shot. Surely then, entanglement is a property of specific systems, rather one of a class of systems.

If you want to read this more substantially (and you have graduate level of mathematics knowledge), quantum resource theories is the area you are looking into.

[1] There are some assumptions on your honesty required here.

[2] Each time using a different random state.

[tooltower]

Kind of? Keep aside quantum mechanics for a second. In any classical experiment that has random outcomes, would you say that the probability distribution is a property of a single system or a bunch?

You can only deduce a distribution from repeated measurements. But most physicists would have no problem talking about a single experiment having many possible outcomes, governed by a probability distribution. It's almost a philosophical question about whether probability means anything in single systems.

It's the same way in quantum mechanics. The effects of entanglement can only be discerned if you take repeated samples. But we still feel okay talking about single systems governed by such entanglement.

[wasabi991011]

Almost, but not quite.

It means something about a specific system, but it can only be verified statistically by producing copies of that system (not "class of systems") en mass.