Is Energy Entanglement Possible?

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Discussion Overview

The discussion centers around the concept of energy entanglement in quantum mechanics, exploring whether two particles can be entangled based on their energy properties. Participants consider theoretical frameworks, potential experiments, and the implications of energy conservation in entanglement generation.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants question the definition of 'energy entanglement' and its implications for experiments.
  • One participant proposes a model involving two-state systems and suggests that a specific entangled state can be formed where both subsystems have equal energies.
  • Another participant argues that while energy conservation is relevant in entanglement generation, it does not directly cause entanglement.
  • Some participants discuss the nature of entangled states, emphasizing that not all two-particle systems are entangled and that entangled states cannot be described by product states.
  • A participant introduces the concept of entanglement between position and spin in a single particle scenario, referencing the Stern-Gerlach experiment.
  • There is a discussion about the mathematical representation of entangled states and the implications of probabilities in these states.
  • Some participants express uncertainty about the relationship between energy eigenvalues and entanglement, suggesting that equal probabilities are not fundamental to the concept of entanglement.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the definition and implications of energy entanglement, with no consensus reached on the nature of entangled states or the mechanisms behind entanglement.

Contextual Notes

Some discussions highlight limitations in understanding the physical mechanisms of entanglement, the dependence on definitions, and the complexities of mathematical representations without resolving these issues.

  • #31
Zafa Pi said:
I would like to propose the following: If a state |ζ⟩ representing multiple particles can't be factored it is fully entangled. If |ζ⟩ can be factored (to lowest terms) but one of its factors also represents multiple particles but it can't be factored then we say |ζ⟩ is partially entangled. We say |ζ⟩ is entangled if it is either fully or partially entangled.
Term "partial entanglement" is already taken. It refers to state vector ##|\psi\rangle=a|00\rangle+b|11\rangle## where |a| and |b| are different.
 
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  • #32
zonde said:
Term "partial entanglement" is already taken. It refers to state vector ##|\psi\rangle=a|00\rangle+b|11\rangle## where |a| and |b| are different.
Too bad for me. But good looking out. How about sortta entangled?
Demystifier said:
I am pretty sure that N&C would say that it consists of two disctinct physical systems.
Given what we've been discussing I am pretty sure you're right. But at the time I read it, it wasn't clear to me at all.
 

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