We take up three questions left open by the induced-Wilson-action companion: quantum dynamical links, composition across a network, and coupling flow. A record channel decohering a quantum link superselects the link's holonomy relative to the boundary frames — not, as first conjectured and then disproved, its conjugacy class. Whether the link is merely superselected or driven to a preferred value is decided by the bath spectrum: a flat-band renewal bath superselects without pinning, a thermal matter bath pins. The induced action's harmonic content decays by an affine law, and fermion back-action threads a chiral connection through link space. Keywords: quantum link models, lattice gauge theory, superselection rules, decoherence, holonomy, open quantum systems, Berry connection, emergent gauge symmetry, quant-ph, hep-lat, hep-th
We take up three questions left open by the induced-Wilson-action companion: quantum dynamical links, composition across a network, and coupling flow. A record channel decohering a quantum link superselects the link's holonomy relative to the boundary frames — not, as first conjectured and then disproved, its conjugacy class. Whether the link is merely superselected or driven to a preferred value is decided by the bath spectrum: a flat-band renewal bath superselects without pinning, a thermal matter bath pins. The induced action's harmonic content decays by an affine law, and fermion back-action threads a chiral connection through link space. Keywords: quantum link models, lattice gauge theory, superselection rules, decoherence, holonomy, open quantum systems, Berry connection, emergent gauge symmetry, quant-ph, hep-lat, hep-th
A network of non-equilibrium information channels, each carrying an internal-symmetry rotation on its transported content, induces on those rotations the structure of a lattice gauge theory. In a two-arm interferometer built from the exactly solvable correlated-injection channel we establish four properties by direct computation: the link acts as a Wilson line; induced scalars are gauge invariant to machine precision; the functionals depend on the link configuration only through the conjugacy class of the loop holonomy; and the induced action is reproduced by a low-order character expansion of Wilson form. Results hold unchanged for SU(2) and SU(3). Keywords: lattice gauge theory, Wilson action, gauge invariance, character expansion, holonomy, emergent gauge symmetry, non-equilibrium steady states, interferometry, hep-lat, hep-th, cond-mat.stat-mech
Lattice gauge theories (LGT) play a central role in modern physics, providing insights into high-energy physics, condensed matter physics, and quantum computation. Due to the nontrivial structure of the Hilbert space of LGT systems, entanglement in such systems is tricky to define. However, when one limits themselves to superselection-resolved entanglement, that is, entanglement corresponding to specific gauge symmetry sectors (commonly denoted as superselection sectors), this problem disappears, and the entanglement becomes well-defined. The study of superselection-resolved entanglement is interesting in LGT for an additional reason: when the gauge symmetry is strictly obeyed, superselection-resolved entanglement becomes the only distillable contribution to the entanglement. In our work, we study the behavior of superselection-resolved entanglement in LGT systems. We employ a tensor network construction for gauge-invariant systems as defined by Zohar and Burrello (2016) and find that, in a vast range of cases, the leading term in superselection-resolved entanglement depends on the number of corners in the partition, that is, corner-law entanglement. To our knowledge, this is the first case of such a corner-law being observed in any lattice system.
In the mediated-access programme a sieve decides which imprints become persistent records. We show the sieve's destination rule is not an extra postulate but descends from the symplectic structure the fiber metric already supplies. A single Kaluza–Klein metric object yields gauge, gravitational, and engagement couplings at once, and Hamilton's equations then orient the flows — a system writes cell invariants while cell angles are read back only as system phases. In the quantum theory a charge-n quantum shifts the mode label by exactly n, and that record is simultaneously the which-path decoherence. Keywords: Kaluza–Klein theory, decoherence, pointer states, quantum measurement, symplectic geometry, holonomy, equivalence principle, quantum Darwinism, hep-th, quant-ph
When reference frames are treated quantum mechanically, the subsystem structure of quantum systems is no longer absolute, but depends on the choice of the quantum reference frame (QRF). This raises a basic question: which dynamical properties are preserved across QRFs, and which depend on the physical reference used to define the system? We study this question in the general setting of open quantum systems. At the operational level, after a QRF transformation, the old reference frame and environmental degrees of freedom may be inaccessible and must therefore be traced out. This motivates the definition of reduced quantum-reference-frame channels: maps that connect the joint description in one frame to the accessible subsystem in another. We characterize their symmetry-constrained structure and define a regime in which a reduced entropy-coherence conservation law holds. We also identify when the induced reduced action on the open system admits a classical interpretation as random frame misalignment, and when it instead reflects quantum reduced-frame effects. We then apply the framework to pure-dephasing dynamics and derive a necessary and sufficient compatibility condition for population preservation. When the frame symmetry commutes with the open system's free Hamiltonian, coherences acquire a multiplicative frame factor, so that locally inferred decoherence rates split into environmental and reference-induced contributions. Ramsey interferometry gives this split a direct operational meaning. Finally, a gravity-motivated dephasing model illustrates how degradation of a phase reference can mimic signatures usually attributed to intrinsic decoherence mechanisms.
A bstract Lattice gauge theories (LGT) play a central role in modern physics, providing insights into high-energy physics, condensed matter physics, and quantum computation. Due to the nontrivial structure of the Hilbert space of LGT systems, entanglement in such systems is tricky to define. However, when one limits themselves to superselection-resolved entanglement, that is, entanglement corresponding to specific gauge symmetry sectors (commonly denoted as superselection sectors), this problem disappears, and the entanglement becomes well-defined. The study of superselection-resolved entanglement is interesting in LGT for an additional reason: when the gauge symmetry is strictly obeyed, superselection-resolved entanglement becomes the only distillable contribution to the entanglement. In our work, we study the behavior of superselection-resolved entanglement in LGT systems. We employ a tensor network construction for gauge-invariant systems as defined by Zohar and Burrello [1] and find that, in a vast range of cases, the leading term in superselection-resolved entanglement depends on the number of corners in the partition — corner-law entanglement. To our knowledge, this is the first case of such a corner-law being observed in any lattice system.
This work formulates and tests a general principle governing when physical records remain accessible under quantum dynamics. Across previous models involving gauge theory, thermalization, closed universes, and scrambling systems, a common structure emerges: some distinctions survive only when the dynamics preserve an observer-accessible information structure. The paper introduces a rigorous definition of records using restricted distinguishability between histories: E_A = − ln F(ρ₀|A, ρ₁|A) and defines protection as the persistence of this distinguishability under an allowed class of quantum channels. The proposed principle is: A record is protected if and only if an observer-accessible Heisenberg fixed-point (peripheral) operator of the allowed channel class distinguishes the histories. The principle is tested against several systems: 1. Covariant quantum channels, where explicit fidelity lower bounds are verified. 2. Many-body localization, showing that protection can arise from emergent quasi-local conserved structures rather than fundamental symmetries. 3. Noiseless subsystems, demonstrating that protected records can exist through operator-algebraic commutants rather than conserved densities. 4. Blind searches over random semigroups, where every protected case contains the predicted fixed-point witness. The work connects quantum records with existing theories of information-preserving structures, superselection, asymmetry, quantum error correction, and emergent conservation laws. The result is a general operator-algebraic framework for understanding why some information survives dynamics while other information becomes inaccessible.