Entanglement in single particle state Is it possible that we have entanglement in different degrees of freedom of a single particle, like spin and linear momentum?
 A: Even though you think of it as a single particle -- each of its different properties like momentum, spin, etc (corresponding to each valid quantum number) sits in a Hilbert space of their own and the possible configurations of a particle sit in a tensor product of those Hilbert spaces.
$$\mathcal{H_{particle}} = \mathcal{H_{momentum}} \otimes \mathcal{H_{spin}} \otimes \ldots $$
Like any other case, when we have a state in some space which can be broken up into subsystems tensored together, we can talk about correlations in those subsystems. If those correlations are quantum mechanical, then of course we will have entanglement -- like any other system you know about.
A: Yes, it is possible and in fact such states also have a fully classical description (coherence theory). Due to this fact, this type of coherence is sometimes referred to as "classical entanglement."
A: Yes, we can have entanglement between different degrees of freedom of the same particle or system.
That is known as ''hybrid entanglement'' and that is experimentally demonstrated also.
Reference: C. Gabriel et al., Hybrid-Entanglement in Continuous Variable Systems, arXiv:1007.1322.
