  We study different aspects of quantum entanglement and its measures,
including entanglement entropy in the vacuum state of a certain Lifshitz scalar
theory. We present simple intuitive arguments based on "non-local" effects of
this theory that the scaling of entanglement entropy depends on the dynamical
exponent as a characteristic parameter of the theory. The scaling is such that
in the massless theory for small entangling regions it leads to area law in the
Lorentzian limit and volume law in the $z\to\infty$ limit. We present strong
numerical evidences in (1+1) and (2+1)-dimensions in support of this behavior.
In (2+1)-dimensions we also study some shape dependent aspects of entanglement.
We argue that in the massless limit corner contributions are no more additive
for large enough dynamical exponents due to non-local effects of Lifshitz
theories. We also comment on possible holographic duals of such theories based
on the sign of tripartite information.
