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The Informational Access Space Indistinguishability, Separability, and the Algebraic Reconstruction of Hidden Structures

Vlasie Catalin Mircea

Published Aug 25, 2026• 0 citations
Publisher
DOI
10.13140/rg.2.2.11783.76968

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Quantum Darwinism and related objectivity frameworks study how information about a quantum system is redundantly recorded in its environment. This preprint studies a downstream selection problem: when several candidate records coexist, which one is public under a specified access channel? The problem is formulated as access-limited quantum hypothesis testing. The global Chernoff distinguishability of a candidate record is compared with the public Chernoff distinguishability after a declared sequence of completely positive trace-preserving access maps. The main result is a sufficient access-algebra separation mechanism: if a broadcast record has extensive distinguishability inside the public access algebra, while a globally stronger encoded record is hidden from that algebra at subextensive rate, then global information density and public distinguishability density have opposite thermodynamic orderings. This is not a definition of objectivity in the sense of Spectrum Broadcast Structure or Strong Quantum Darwinism; it is an operational separation theorem for a declared public decision problem. The preprint gives a random-linear access-algebra construction and controlled realizations based on code distance, local circuits, operator spreading, and protected Hamiltonian access algebras.
Physical restrictions on operations can make quantum coherence inaccessible. Quantifying off-diagonal density matrix elements in a chosen basis alone does not reveal which information is hidden by each restriction. To distinguish their effects, we describe physical restrictions through subalgebras of accessible observables. The associated trace-preserving conditional expectations unify two reconstruction principles: each gives both the maximum-entropy state compatible with the accessible data and the closest state in the corresponding subalgebra in relative entropy. We apply this framework to anyonic systems to separate the contributions from local-charge superselection and non-Abelian fusion rules. We prove that the charge-line severing map is the conditional expectation onto the local-product subalgebra. It is completely positive and quantum-trace-preserving, and uniquely reconstructs a state in this space from all local-product expectation values. The hierarchy of measurement restrictions then separates total bipartite coherence into three nonnegative contributions: coherence between local charges, inaccessible fusion information, and conventional coherence. The first two decompose the anyonic charge entanglement and distinguish the effects of local-charge superselection from the remaining fusion information. Finally, we relate basis-independent measures of anyonic coherence to entanglement. For pure anyonic states with vacuum total charge, the optimized total and correlated coherence equal the total and conventional relative-entropy entanglement, respectively.