Can particles be entangled on any property having more than two states?

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Discussion Overview

The discussion centers on whether particles can be entangled based on properties that have more than two states, specifically focusing on photons, electrons, and other particles. The scope includes theoretical considerations of entanglement and the nature of quantum states.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions if entanglement can occur on properties with more than two states, using spin as an example, which only has two states.
  • Another participant suggests that entanglement is possible through position and momentum, which can take on an infinite number of states, thus supporting the idea of entanglement beyond two states.
  • A third participant agrees that position and momentum are observables that can exhibit entanglement, reinforcing the previous point.
  • Another participant mentions the possibility of entanglement in continuous variables, citing a specific study on three-photon energy-time entanglement as an example of this phenomenon.
  • One participant reiterates the idea that momentum and position have infinite states, affirming their earlier stance on the possibility of entanglement.

Areas of Agreement / Disagreement

Participants generally agree that entanglement can occur with properties that have more than two states, particularly through position and momentum. However, the discussion includes varying perspectives on the specifics and implications of these claims.

Contextual Notes

The discussion does not resolve the complexities of creating entangled states in continuous variables, nor does it clarify the conditions under which such entanglement can be achieved.

San K
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can particles be entangled on any property having more than two states?

Photons can be entangled on spin. however spin has only two states:

Up or down, plus or minus

So the question is:

is there any property (having more than two states) on which photons/electrons/bucky-ball can be entangled?

note: measuring the spin in different directions is still dealing with only a two-state spin.
 
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My gut feeling is yes. If you have a photon decomposing into an electron and a positron, then (in the centre of mass frame), the two particles will move apart with the same momentum. If we then measure the position of one of the particles, then we must disturb the momentum of the other - otherwise it would be possible to measure the momentum of the other particle and hence break Heisenberg's Uncertainty Principle, knowing both the position and momentum of at least one of the particles.

Since the momentum and position has an infinite number of states (infinite is greater than 2), then my answer is yes. However, I'd love someone else to add their viewpoint on this.
 
Yes, as mentioned position and momentum are examples of observables with more than 2 states. There can be entanglement on those.
 
Sure, you can even have entanglement on continuous variables, although it is non-trivial to create such a state. Check for example the paper on three-photon energy-time entanglement in the upcoming issue of Nature Physics where the Jennewein group managed to create tripartite continuous-variable entanglement between three separated particles (Shalm et al., Nature Physics (2012) doi:10.1038/nphys2492).
 
DeShark said:
Since the momentum and position has an infinite number of states (infinite is greater than 2), then my answer is yes. However, I'd love someone else to add their viewpoint on this.

Thanks DeShark, DrChinese and Cthuga.
 

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