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Complexity in algebraic QFT
Stefan Hollands and Alessio RanalloAbstract
We consider a notion of complexity of quantum channels in relativistic continuum quantum field theory (QFT) defined by the distance to the trivial (identity) channel. Our distance measure is based on a specific divergence between quantum channels derived from the Belavkin-Staszewski (BS) divergence. We prove in the prerequisite generality necessary for the algebras in QFT that the corresponding complexity has several reasonable properties: (i) the complexity of a composite channel is not larger than the sum of its parts, (ii) it is additive for channels localized in spacelike separated regions, (iii) it is convex, (iv) for an
The main technical tool in our work is a new variational principle for the BS divergence.
- Received:
- 21.02.23
- Published:
- 24.02.23
- MSC Codes:
- 81P45, 81T05, 46L10
- Keywords:
- complexity theory, Quantum Field Theory, Operator algebras