It is well known that, even the simplest states within the simplest field theories, are highly entangled. The main support for this fact comes from calculations of entanglement entropy between a region of space and its complement. I find two uncomfortable facts in the calculation of such entropy: (i) The result is actually infinite, and a regulator is needed to extract a finite quantity out of it; and more important, (ii) it involves infinite regions of space and infinitely many degrees of freedom of the field. During the last months, I have been thinking of a more tangible way of quantifying entanglement in quantum field theories, involving only a finite number of degrees of freedom, finite regions of space and quantities that are directly measurable.
In this talk, I will summarize the understanding I have achieved so far, both for Minkowski and de Sitter spacetimes. This is work in progress, and I will especially emphasize what I do not understand yet, aiming to receive feedback and provoke discussions.