# Are all bound states entangled?

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?
• 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. Oct 9, 2019 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. Oct 9, 2019 at 23:53
• @KFGauss correct, agree, that is what I wrote. Oct 10, 2019 at 2:08
• 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. Oct 10, 2019 at 3:53
• @LewisMiller different particles can be entangled too. physics.stackexchange.com/questions/224317/… Oct 10, 2019 at 15:51