Are photons created in Spontaneous Parametric Down-Conversion (SPDC) intrinsically entangled? If, yes, why to construct all complicated interferometers (Mach-Zender, Sagnac) around it?
Is it critical that the photons not be entangled in any degrees of freedom other than the one encoding the quantum information?
thank you Vlad
Most of the photon pairs produced in Spontaneous Parametric Down-Conversion (SPDC) are entangled. There are nuances to that statement. For example, Type I PDC requires 2 crystals rather than the usual 1 crystal for Type II PDC. Also, the pairs must be captured in such a way that they are sufficiently indistinguishable. Some of the produced pairs won't meet this criteria very well, and so their entanglement fidelity will be lower. (Note that entanglement is not necessarily "all or nothing".)
Also, the entanglement can exist on one or more bases (polarization, momentum, wavelength, etc). There is no requirement that entanglement be limited to one degree of freedom for the resulting entangled photons (sometimes called a biphoton) to be useful.
As to why interferometers are used: this is specific to the experiment being performed. Often they are used to demonstrate a particular element of quantum mechanics, such as the idea that there are contributions to the predicted result that come from both arms even when a single photon is present. The entangled partner can be used to "herald" the other one's presence, or it can have an additional test performed on it.
