Do equivalent quantum states imply entanglement?

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Discussion Overview

The discussion centers around the relationship between identical quantum states and entanglement, exploring whether two particles that share the same quantum states can be considered entangled without prior interaction. The scope includes conceptual clarifications and theoretical implications of quantum mechanics.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions whether two particles that are probabilistically identical but have never interacted can be considered entangled, suggesting that action on one might affect the other in a similar manner to traditionally entangled particles.
  • Another participant asserts that if two particles share the same quantum state, they cannot be entangled, citing the definition of entanglement which requires that the total wavefunction cannot be factored into individual wavefunctions.
  • A participant expresses uncertainty about their understanding of the topic and seeks further reading suggestions.

Areas of Agreement / Disagreement

There is disagreement regarding whether identical quantum states imply entanglement, with one viewpoint suggesting they do not lead to entanglement and another proposing a potential connection. The discussion remains unresolved.

Contextual Notes

The discussion highlights the complexity of defining entanglement and the implications of identical quantum states, with participants not fully agreeing on the definitions and consequences involved.

pinkumbra
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Assume there are two particles which share the same quantum states (that is, if I understand correctly, both are probabilistically identical), but have not been through the process of entanglement. Let's assume they never interacted in any dimensions, they just happened to be identical. Would they thus be entangled because they're identical? That is, would action on one affect it's partner in the same way if it was traditionally entangled?
 
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Am I thinking about this the wrong way?

Perhaps someone should throw me a book suggestion.
 
pinkumbra said:
Assume there are two particles which share the same quantum states (that is, if I understand correctly, both are probabilistically identical), but have not been through the process of entanglement. Let's assume they never interacted in any dimensions, they just happened to be identical. Would they thus be entangled because they're identical? That is, would action on one affect it's partner in the same way if it was traditionally entangled?

If they have the same quantum state, they cannot be entangled. By definition, an entangled state is one which cannot be factored into a product of two one-particle state wavefunctions. If the two particles are exactly in the same quantum state, th etotal wavefunction is simply the product of those two identical wavefunctions and is therefore not an entangled state.
 
Righto, thank you.
 

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