Why are interacting states necessarily entangled?

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    Entangled States
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Discussion Overview

The discussion revolves around the nature of states in composite systems of interacting particles, specifically addressing why interacting particles are often considered to be in entangled states rather than product states. Participants explore the conditions under which particles may remain in product states despite interactions and the implications of such interactions on entanglement.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant questions why interacting particles are always considered to be in entangled states, noting that non-interacting particles can be represented as product states.
  • Another participant argues that interacting particles can indeed be in product states, using the example of two ions in an ion trap that interact via Coulomb forces but may still be in a product state.
  • A later reply acknowledges a misunderstanding about the relationship between interaction and entanglement and seeks clarification on the physical conditions necessary for particles to become entangled upon interaction.
  • Another participant states that most states in the composite Hilbert space of two systems are entangled and suggests that if particles interact while initially in a product state, it is more likely they will evolve into an entangled state over time.
  • This same participant introduces the concept of decoherence, explaining that if particles remain in a product state, the interaction with an external system (like the ion trap) may lead to entanglement between the particles and the trap instead of between the particles themselves.

Areas of Agreement / Disagreement

Participants express differing views on whether interacting particles can be in product states, leading to an unresolved discussion regarding the conditions under which entanglement arises from interactions.

Contextual Notes

There are references to specific physical systems (like ion traps) and concepts (such as decoherence) that may influence the understanding of entanglement and interaction, but these are not fully resolved within the discussion.

metroplex021
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It just occurred to me that I don't know why composites of interacting particles are always in entangled -- as opposed to mere product -- states. Obviously if they are not interacting we will just represent them as being in a product state; but why is it that being in a product state entails not interacting?

Any comments appreciated! Thanks!
 
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You have to clarify what you mean I think. I don't see any problem with particles being interacting and in a product state at the same time. A straightforward example is 2 ions trapped in the same ion trap. They would have to be considered as interacting because they affect each other with mutual coulomb forces, but they can surely be in a product state.

Where you think of some special situations or interactions?
 
Huh! I was wrong about that then. Thanks for putting me straight. Can I then ask: does anyone know what physical conditions have to be fulfilled for a pair of particles to go into an entangled state upon interaction? Thanks to anyone who can help!
 
metroplex021 said:
does anyone know what physical conditions have to be fulfilled for a pair of particles to go into an entangled state upon interaction?
There are no special physical conditions. Most states in the composite Hilbert space of two single systems are entangled states. If the particles interact and we initially prepare a product state, it is simply much more likely that at an arbitrary later time, the product state has evolved into an entangled state instead of another product state.

In the example of the ion trap, we have to consider an additional third system: the trap. If the particles are in a product state at all times, this means that the interaction with the trap is such that it destroys the entanglement of the particles on a short time scale (decoherence). Entanglement then exists between the particles and the trap and not between the particles themselves.
 
Last edited:
Perfect, thank you. Much appreciated!
 

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