English

Spin networks of quantum channels

General Relativity and Quantum Cosmology 2026-02-13 v1 High Energy Physics - Theory Quantum Physics

Abstract

Spin networks in Loop Quantum Gravity are traditionally described by unitary holonomies corresponding to noiseless transformations. In this work, we extend this framework to incorporate general quantum channels that model effects of environment, which can become significant at the Planck scale. Specifically, we demonstrate that the transformation properties of Kraus operators, which define completely positive trace-preserving (CPTP) maps, are consistent with the gauge invariance of spin networks. This enables the introduction of generalized spin network states that can be expressed in terms of the Kraus operators. Furthermore, the associated notion of an inner product is proposed, allowing for introduction of the Hilbert space. We illustrate these constructions with examples involving a Wilson loop and a dipole network.

Keywords

Cite

@article{arxiv.2602.12145,
  title  = {Spin networks of quantum channels},
  author = {Bartosz Grygielski and Jakub Mielczarek},
  journal= {arXiv preprint arXiv:2602.12145},
  year   = {2026}
}

Comments

13 pages, 5 figures

R2 v1 2026-07-01T10:34:03.968Z