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referframe

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Is that correct?

As always, thanks in advance.

- Thread starter referframe
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- #1

referframe

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- 15

Is that correct?

As always, thanks in advance.

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- #3

Ken G

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kith

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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.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.

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.

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