Subsystems in gauge theories
For specified gauge-invariant operations and boundary access, characterize distillable resources of spatial subsystems and prove when their continuum predictions are regulator independent; compare different access models without assuming a unique factorization
Problem statement
For specified gauge-invariant operations and boundary access, characterize distillable resources of spatial subsystems and prove when their continuum predictions are regulator independent; compare different access models without assuming a unique factorization.
Lean 4
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Background
In a gauge theory the Gauss-law constraint entangles degrees of freedom across any spatial boundary, so a region's Hilbert space does not factorize as a simple tensor product. Defining 'the entanglement entropy of a region' requires a choice — an algebra with a nontrivial center, or the introduction of boundary 'edge modes' — and different choices give different answers.
What is known: Casini–Huerta–Rosabal formulated the algebraic center-choice approach; Donnelly and Donnelly–Freidel developed boundary edge-mode descriptions. Entropy decompositions depend on the algebra and access model and, in non-Abelian theories, can include representation-dependent terms as well as classical flux-sector uncertainty. Van Acoleyen et al. give an operational lattice distillation analysis including non-Abelian gauge groups: not every extended-Hilbert-space entropy contribution is distillable by gauge-invariant local operations.
What remains is controlled passage from a stated lattice access model to continuum gauge fields, with dynamical matter, boundary resources and finite-energy operations explicitly accounted for. Compare inequivalent definitions by the tasks they permit, rather than demanding that physically different access models share one canonical entropy. Related: QF8, QF11, F7.
Progress & source assessment
Source catalogue review: 4 September 2026. Improved indicates partial progress, including qualified preprint claims.
Recorded progress
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