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arXiv · 2302.10013

Complexity in algebraic QFT

Stefan Hollands·Alessio Ranallo
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Abstract

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 $N$-ary measurement channel it is $\log N$, (v) for a conditional expectation associated with an inclusion of QFTs with finite Jones index it is given by $\log (\text{Jones Index})$. The main technical tool in our work is a new variational principle for the BS divergence.

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Stefan Hollands, Alessio Ranallo. 2023-02-20. Complexity in algebraic QFT. https://doi.org/10.1007/s00220-023-04855-x

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