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We study different aspects of quantum entanglement and its measures,including entanglement entropy and mutual information in the vacuum state of a certain Lifshitz free scalar theory?We present simple intuitive arguments based on the non-locality of this theory, supported by strong numerical evidences in $(1+1)$ and $2+1)$-dimensions, that the scaling of entanglement in such theories depends on the value of the dynamical exponent as a characteristic parameter of the theory. The scaling is such that in the Lorentzian limit it gives an area law and in the large dynamical exponent limit it tends to a volume law. We also study some aspects of entanglement depending on the shape of the entangling region in $(2+1)$-dimensions including corner contributions. We show that corner contributions are no more additive due to non-locality of Lifshitz theories. We also comment on possible holographic duals of such theories based on the sign of tripartite information.
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