This note extends the record-classification framework into a two-dimensional lattice gauge theory by studying pure Z2 gauge theory on finite tori. Using exact diagonalization in winding sectors, the work tests how quantum information is stored, distributed, and destroyed across different gauge phases. The classification survives and becomes sharper. The constraint record becomes a topological redundancy: any enclosing loop can recover the enclosed charge parity exactly at every coupling and in every phase, as a direct consequence of Gauss's law. String records appear only where confinement localizes flux into physical strings. The toric-code sector qubit forms a matter-blind record class, preserved in the topological phase but destroyed by confinement. Across the phase diagram, different records migrate or disappear, but the constraint record remains invariant. The study also identifies an important boundary case: antipodally placed charges do not produce a missing record, but an undefined local record because degenerate winding routes prevent a unique assignment. The results show that quantum records in gauge theories are determined by the underlying constraint structure and topology. Some information becomes redundantly accessible through global constraints, some becomes localized through confinement, and some survives only as nonlocal topological information. All results are obtained through exact finite-lattice calculations with documented verification checks and reproducibility data.
This note extends the record-classification framework into a two-dimensional lattice gauge theory by studying pure Z2 gauge theory on finite tori. Using exact diagonalization in winding sectors, the work tests how quantum information is stored, distributed, and destroyed across different gauge phases. The classification survives and becomes sharper. The constraint record becomes a topological redundancy: any enclosing loop can recover the enclosed charge parity exactly at every coupling and in every phase, as a direct consequence of Gauss's law. String records appear only where confinement localizes flux into physical strings. The toric-code sector qubit forms a matter-blind record class, preserved in the topological phase but destroyed by confinement. Across the phase diagram, different records migrate or disappear, but the constraint record remains invariant. The study also identifies an important boundary case: antipodally placed charges do not produce a missing record, but an undefined local record because degenerate winding routes prevent a unique assignment. The results show that quantum records in gauge theories are determined by the underlying constraint structure and topology. Some information becomes redundantly accessible through global constraints, some becomes localized through confinement, and some survives only as nonlocal topological information. All results are obtained through exact finite-lattice calculations with documented verification checks and reproducibility data.
Quantum Darwinism explains classical objectivity through the redundant proliferation of records in an environment. This note studies that mechanism inside a gauge theory, where Gauss's law constrains which records can exist and where they can be stored. Using exact lattice Schwinger model calculations with both open and periodic boundaries, including the Wilson-line rotor, this work shows that record redundancy is determined by the relation between information and gauge constraints. Three fundamental record classes are identified. First, unscreenable charges produce perfectly redundant records: every accessible downstream region can read the same information because the constraint itself distributes the record without requiring copying dynamics. Second, screened charges produce bilocal records, with information divided between the screening cloud and the boundary-delivered image while intermediate regions remain blind. Third, symmetry-breaking order produces graded redundant records, while topological flux records represent the opposite extreme: globally distinguishable but invisible to local matter fragments. The study also reveals a constraint-induced discordant split. In the flux sector, mutual information can remain large while readable evidence is almost absent, showing that a gauge theory can contain correlations that no local fragment can convert into classical information. The central conclusion is that classical objectivity in gauge theories is not determined only by environmental interaction. It is controlled by the structure of the constraints: Gauss's law decides which records can be broadcast, localized, or hidden. All results are obtained through exact diagonalization with independent verification checks and documented numerical convergence tests.
This note removes the open-boundary constraint from the lattice Schwinger model and studies the periodic theory with its physical Wilson-line zero mode. The goal is to determine which features of the previous lattice results belong to the gauge theory itself and which were caused by the boundary. Using exact diagonalization of the periodic lattice model with fermions and flux degrees of freedom, the study reveals four main results. The transition is restored: the mass-gap collapse and the critical response reappear, with the mass-direction evidence developing an interior peak near the transition region. The θ-lock is recovered at zero fermion mass, with the sector energy sensitivity strongly reduced compared with the open-boundary case, while the mass-induced unlock follows the expected perturbative behavior and becomes critically enhanced near the transition. The transition-amplifier law also returns: sector evidence grows monotonically with the mass deformation, showing that the open-boundary inversion was a boundary artifact caused by pinning both sectors to a single vacuum. The central result is a record-migration law. In the massless theory, the θ-record is stored mainly in matter correlations and can be accessed through charged endpoints of spatial cuts. In the massive broken phase, the record moves into the topological flux sector: the competing vacua differ by a Wilson-loop flux, making the information invisible to purely matter-based local observers. This establishes how the location of quantum information changes across phases of an interacting gauge theory: symmetry breaking does not only create records, it determines who can access them. The results are obtained within the finite periodic lattice framework, with bounded system sizes, rotor truncation checks, and no continuum extrapolation.
This work tests whether the theory of quantum records survives the transition from finite lattice models to continuum quantum field theory. Using a free scalar field in 1+1 dimensions with two histories differing by a localized classical source, the record accessible to a spatial region is expressed exactly through the fidelity of equal-covariance Gaussian states. Four principal results are established. First, the continuum record functional is verified against direct truncated-Fock-space Uhlmann fidelity calculations with agreement at approximately 10^−10. Second, the lattice record converges monotonically toward the exact continuum mode-sum result under refinement from 256 to 2048 lattice sites, demonstrating that the framework is not a lattice artifact. Third, a continuum lock law is found: record evidence measured a distance L from a localized source decays as exp(−2mL), with the fitted decay rate agreeing with 2m to high precision. This identifies the finite-volume suppression observed in earlier discrete models as the lattice manifestation of a continuum correlation-length law. Fourth, the distinction between constraint records and arrangement records survives the continuum limit. As the screening length diverges, the ratio between net-charge and zero-charge rearrangement records grows approximately as 1/m², causing the constraint-class record to dominate without bound. An exploratory study of disjoint regions also finds uniformly subadditive record evidence, consistent with redundant access to a common source through continuum vacuum correlations. The results establish the first continuum realization of the record framework in an exactly controlled quantum field theory. The present analysis is restricted to a free scalar field in 1+1 dimensions and coherent mean-shift histories; interacting fields, gauge theories, massless limits, higher dimensions, and gravity remain open.
We develop a comprehensive framework for constructing quantum error correcting codes (QECCs) from Abelian lattice gauge theories (LGTs) using quantum reference frames (QRFs) as a unifying formalism. We consider LGTs with arbitrary compact Abelian gauge groups supported on lattices in arbitrary numbers of spatial dimensions, and we work with both pure gauge theories and theories with couplings to bosonic and fermionic matter. The codes that we construct fall into two classes: First, Gauss law codes identify the code subspace with the full gauge-invariant sector of the theory. In models with matter coupled to gauge fields, these codes inherit a natural subsystem structure in which gauge-invariant Wilson loops and dressed matter excitations factorize the code space. Second, vacuum codes restrict the code subspace to the matter vacuum sector within the gauge-invariant subspace, yielding codes where errors correspond to gauge-invariant charge excitations rather than to violations of the Gauss law. Despite their distinct setup, we show that when the gauge group is finite, vacuum codes are unitarily equivalent to pure gauge theory Gauss law codes, and that when the group is continuous, this is only true upon a charge coarse-graining of the vacuum code. In all cases, QRFs provide a systematic apparatus for fully characterizing the codes' algebraic structures and correctable error sets. For clarity, we illustrate our general results in Z2-gauge theory, as well as in scalar and fermionic QED. These findings offer fundamental insights into the parallelism between quantum error correction and gauge theory and point toward practical advantages for simulating LGTs on noisy quantum devices.
It is now widely recognized that the toric code is a pure gauge-theory model governed by a projective Hamiltonian with topological orders. In this paper, we extend the interplay between quantum information system and gauge-theory model from the viewpoint of subsystem code, which is suitable for gauge systems including matter fields. As an example, we show that Z2 lattice gauge-Higgs model in (2+1)-dimensions with specific open boundary conditions is nothing but a kind of subsystem code. In the system, Gauss-law constraints are stabilizers, and order parameters identifying Higgs and confinement phases exist and they are nothing but logical operators in subsystem codes residing on the boundaries. Mixed anomaly of them dictates the existence of boundary-zero modes, which is a direct consequence of symmetry-protected topological order in Higgs and confinement phases. After identifying phase diagram, subsystem codes are embedded in the Higgs and confinement phases. As our main findings, we give an explicit description of the code (encoded qubit) in the Higgs and confinement phases, which clarifies duality between Higgs and confinement phases. The degenerate structure of subsystem code in the Higgs and confinement phases remains even in very high-energy levels, which is analogous to notion of strong-zero modes observed in some interesting condensed-matter systems. Numerical methods are used to corroborate analytically-obtained results and the obtained spectrum structure supports the analytical description of various subsystem codes in the gauge theory phases.
We calculate the properties of a one-dimensional Z2 lattice gauge theory in different Gauss-law sectors, corresponding to different configurations of static charges, set by the orientations of the gauge spins. Importantly, in quantum simulator experiments these sectors can be accessed without adding any additional physical particles or changing the Hamiltonian: the Gauss-law sectors are simply set by the initial conditions. We study the interplay between conservation laws and interactions when the static charges are chosen to form periodic patterns. We classify the different Gauss-law sectors and use the density matrix renormalization group to calculate the ground-state compressibility, density profiles, charge-density-wave order parameters, and single-particle correlation functions as a function of matter density. We find confined and deconfined phases, charge density waves, correlated insulators, and supersolids.