Entanglement Between Different Types of Particles?

[LarryS]

From what I have read so far, it seems as though entanglement can only exist between particles of the same type (2 photons, 2 electrons, etc.) - that their Hilbert spaces must be compatible and of the same dimension.

Is that correct?

As always, thanks in advance.

 

[xts]

All entanglement experiments were performed with identical particles. But you may (theoretically) entangle parameters of different particles. I see no reason why, e.g., spins of electron and proton should not be entangled.

 

[Ken G]

And I think positrons/electrons are a common topic for entanglement gedankenexperiments, like the Greene version of the EPR paradox (http://en.wikipedia.org/wiki/EPR_paradox). In a way its cleaner-- identical particles exhibit a second form of "entanglement" that has to do with their indistinguishability, gives us the Pauli exclusion principle (for fermions), and is a bit different from what people usually mean by quantum entanglement.

 

[kith]

From what I have read so far, it seems as though entanglement can only exist between particles of the same type (2 photons, 2 electrons, etc.) - that their Hilbert spaces must be compatible and of the same dimension.

What do you mean by "compatible" Hilbert spaces? Mathematically, a composite quantum system with Hilbert spaces H1 and H2 is described by the tensor product H1⊗H2 which does not require the spaces to be of the same dimension. For example, the spatial Hilbert space of a free electron has the dimension infinity while its spin Hilbert space has the dimension 2.

Entangled two-particle-states typically look like |a1>⊗|b1> + |a2>⊗|b2>. The important property here is that when particle a is in state |a1>, particle b is in state |b1> with certainty. Not that the states |a> and |b> live in the same Hilbert space.