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In QM, a bound state is a special state of a particle subject to ta potential such that the particle tends to remain localized in space.

The potential may be external or it may be the result of the presence of another particle; in the latter case, one can equivalently define a bound state as a state representing two or more particles whose interaction energy exceeds the total energy of each separate particle.

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

So basically all bound states of particles need energy to separate the parts.

Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles are generated, interact, or share spatial proximity in ways such that the quantum state of each particle cannot be described independently of the state of the others, even when the particles are separated by a large distance.

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

Now entanglement is defined by sharing spatial proximity in some cases (in ways such that the quantum state of each particle cannot be described independently of the state of the others).

Based on the definitions, entangled particles might not create a bound system, because for example two entangled photons that fly apart, do not need energy to be separated.

But a bound system of particles might be entangled, but I am not sure if it is always the case, so that all bound systems are made up of entangled parts. For example, the constituents of an atom, the quarks that make up the proton and neutrons, and the electrons are creating a bound system. But are all the parts (quarks and electrons) entangled too?

Question:

  1. Are all bound systems (QM) entangled too?
Árpád Szendrei
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    Two entangled photons can be made to be arbitrarily far away from each other. Entanglement is non-local and not necessarily related to space. You can entangle things by getting them close to each other, but that is not a necessary condition. – KF Gauss Oct 09 '19 at 23:53
  • Since photons can be entangled but cannot be bound, the answer to the second half of the question in the title is No: all entangled systems are not bound. – G. Smith Oct 09 '19 at 23:53
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    @KFGauss correct, agree, that is what I wrote. – Árpád Szendrei Oct 10 '19 at 02:08
  • @G.Smith yes, you are correct, that is what I wrote. – Árpád Szendrei Oct 10 '19 at 02:08
  • why the downvote? – Árpád Szendrei Oct 10 '19 at 02:08
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    I think you should change the title to "Are all bound states entangled?". It seems like you already know that not all entangled states are bound. – KF Gauss Oct 10 '19 at 03:53
  • Entanglement is a short hand way of saying: there exists a quantum mechanical description of the system, where the phases between different $Ψ$ are retained . It is the retention of phases , not the energies that make it necessary to describe a system quantum mechanically. – anna v Oct 10 '19 at 04:23
  • @KFGauss thank you I edited. – Árpád Szendrei Oct 10 '19 at 15:44
  • Also particles need to be identical to be entangled. – Lewis Miller Oct 10 '19 at 15:49
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    @LewisMiller different particles can be entangled too. https://physics.stackexchange.com/questions/224317/entanglement-of-different-types-of-particles-possible – Árpád Szendrei Oct 10 '19 at 15:51
  • to be clear, you are not referring to bound entanglement, which is a notion that has nothing to do with the idea of "spatial localisation" that you are referring to here, correct? I ask because the question in the title would make perfect sense with this meaning of the word "bound states" (and the answer would be an easy yes) – glS Oct 12 '19 at 18:37
  • it's not clear what kind of entanglement you are referring to here though. Entanglement between (some degree of freedom of) different particles/parties, or "entanglement" between different degrees of freedom of the same particle. Also, almost anything is "bounded" in some way or another (or at least anything of practical relevance), in the sense that you can alway (generally) describe a given particle as being bounded to stay within some spatial boundaries – glS Oct 12 '19 at 18:51
  • @glS I am referring to bound systems like an atom, where quarks and electrons are bound (you need energy to separate them) and entanglement between (some degree of freedom of) different particles/parties. – Árpád Szendrei Oct 12 '19 at 20:35

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I intentionally didn't read the comments below to see if I could figure it out myself. So I'll give it a try.

Entanglement surely doesn't apply to bound states. In bound states, each state can be described independently of the other states. Of course, you have to take their interactions in account, which means they depend on each other but only in the sense that they interact with each other.

That means that if you could measure the state in which, for example, a certain electron, in a "heavy" atom finds itself (even if they are indistinguishable in each shell, which doesn't imply entanglement either) none of the other constituents will instantaneously jump into a certain state, because of the simple fact that all the constituents already find themselves in a certain state because they continuously (which is quantum-mechanically wrongly put, but that's of little importance in this context) interact with each other.

So in whatever bound states one is interested, it are exactly these interactions which are the cause of non-entanglement.

Two electrons, for example, can't find themselves in a superimposed state, insofar their position is concerned. If you measure the position of one of them when they are far apart from each other then the other electron will not instantaneously (even though this is a somewhat vague notion, but I'm sure you know what I mean) jump in a correlated position, because their positions can't be correlated because of the distance between them. It's different for their spins though. They stay correlated (entangled) all the way because the spins don't depend on the distance between the electrons.

This may seem very strange at first sight (or spooky, as Einstein called it) but it is actually quite logical when you think a bit (or a lot) deeper about it.

Deschele Schilder
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