# Are all properties entangled when one property is entangled?

When one or more particles are quantum entangled by say their spin property, do their other measurable properties (e.g., momentum, polarization, whatever?) become entangled as well?

No, other properties do not necessarily become entangled.

Example: You can take twin photons from type-II parametric down conversion. These two photons are entangled in energy and momentum, but not in polarization.

$$\left|\psi\right>=\left|0\right>+\sum_{k,k'}g(\omega_{ok})\delta(\omega_{ok}+\omega_{ek'}-\omega_p)h(L\Delta_{kk'})\hat a^\dagger_{ok}\hat a^\dagger_{ek}\left|0\right>$$
The delta function and $h(x)$ result in entanglement of energy and momentum respectively, where the part determining the polarization is written in a product of the two polarizations ($o$ for ordinary and $e$ for extraordinary polarization).
• Doesn't there exists types of entanglements, where more $2$ properties are simultaneously entangled?For example,hyperentangled states or entanglement duality "iopscience.iop.org/1367-2630/16/8/08301". – WInterfell Mar 22 '15 at 12:02