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This talk will be devoted to systematically examining certain subtleties in definitions of entanglement entropy. The methods developed here are versatile and apply to many common theories, from spin systems and scalar theories to fermions and gauge theories. To define the entropy associated to a region in each of these theories, two choices must be made: the algebra of operators of interest in the region (i.e. the type of boundary conditions at the entangling edge), and the measure of entropy of this algebra. I will show which choices correspond to the entanglement entropies commonly calculated using QFT and holographic methods, and I will argue that understanding these “ambiguities” can teach us valuable lessons about holographic bulk reconstruction.

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