Entropy of a subalgebra of observables and the geometric entanglement entropy

Eugenio Bianchi, Alejandro Satz

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


The geometric entanglement entropy of a quantum field in the vacuum state is known to be divergent and, when regularized, to scale as the area of the boundary of the region. Here, we introduce an operational definition of the entropy of the vacuum restricted to a region; we consider a subalgebra of observables that has support in the region and a finite resolution. We then define the entropy of a state restricted to this subalgebra. For Gaussian states, such as the vacuum of a free scalar field, we discuss how this entropy can be computed. In particular, we show that for a spherical region we recover an area law under a suitable refinement of the subalgebra.

Original languageEnglish (US)
Article number085001
JournalPhysical Review D
Issue number8
StatePublished - Apr 15 2019

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)


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