Local quantum physics versus (relativistic) quantum mechanics: thermal- versus information theoretic- entanglement and the origin of the area law for \"localization entropy\".

          @misc{ pirsa_PIRSA:08080004,
            doi = {10.48660/08080004},
            url = {https://pirsa.org/08080004},
            author = {Schroer, Bert},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Local quantum physics versus (relativistic) quantum mechanics: thermal- versus information theoretic- entanglement and the origin of the area law for \"localization entropy\".},
            publisher = {Perimeter Institute},
            year = {2008},
            month = {aug},
            note = {PIRSA:08080004 see, \url{https://pirsa.org}}
          }
          

Abstract

The fundamentally different localization concepts of QT, i.e. the Born-(Newton-Wigner) localization of (relativistic) QM as compared with the causal localization (modular localization) of QFT, lead to significant differences in the nature of local observables and affiliated states. This in turn results in a rather sharp distinction between a tensor-factorization and information-theoretic entanglement in QM on the one hand, and a more radical \"thermal entanglement” responsible for an area law for localization entropy. These surprising differences can be traced back to the very different nature of the localized operator algebras in QFT: they are all isomorphic (independent of the localization region) to one abstract \"monad\" (borrowing terminology from Leibniz) and the full reality of QFT (including its symmetries) is contained in the positioning of a finite rather small number (2 for chiral theories, 6 for d=1+3,...) within a joint Hilbert space. It is an important open question to what extend such positional characterizations (where the individual monads are void of any physical properties which reside fully in their relative placements) can be generalized to CST or QG.