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1

It is a tensor product. (At least it always was when I encountered such notations, I can't speak with authority about SPDC specifically) Let $\mathcal{H}_1$ be the Hilbert space of polarization states for a single photon. Then the space of states for a two photon system is $\mathcal{H}_2 = \mathcal{H}_1 \otimes \mathcal{H}_1$, and the state you consider in ...

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As Trimok says, every photon - and for that matter, any physical two-level system - is immediately a qubit. In other words, qubits are abundant in nature and not very interesting by themselves. Also, a qubit alone is not entangled. The interesting part is, what you can do with your qubit: Can you create a qubit in always the same state? Can you entangle a ...

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Any photon (pure) state may be described by a q-bit formalism: $$|photon\rangle = \alpha |0\rangle + \beta|1\rangle$$ where $|0\rangle$ and $|1\rangle$ represent the two possible polarizations of the photon. So, any photon "is" a q-bit. You don't have to "create" q-bits. Just prepare photons is some state. An entangled state of $2$ photons may be ...

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Yes, this is possible. The device that makes this possible is called a polarizing beam splitter, which will transmit or reflect light according to its polarization. Thus, it will split diagonal or circular light into its horizontal and vertical components, and when used in reverse it will undo the process (it has to). Note, however, that you will in general ...

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