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

1. Dec 10, 2012

### San K

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.

2. Dec 10, 2012

### DeShark

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.

3. Dec 10, 2012

### DrChinese

Yes, as mentioned position and momentum are examples of observables with more than 2 states. There can be entanglement on those.

4. Dec 10, 2012

### Cthugha

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).

5. Dec 10, 2012

### San K

Thanks DeShark, DrChinese and Cthuga.