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Canonical Emergence of the Density Operator from Normalized Probabilistic Structure
2026-03-06
We present a minimal, representation-invariant route from normalized probabilistic structure to operator state description. Starting from probability assignments to admissible effects, we show how simplex-type (context-fixed) descriptions embed into the convex set of density operators as the minimal basis-invariant closure. The key representation is the trace pairing p(E) = Tr(ρE), where ρ ⪰ 0 and Trρ = 1. We also formalize composition and marginalization: correlations are encoded by joint states ρAB, while locally accessible statistics are represented uniquely by reduced states ρA = TrB(ρAB). The paper is intentionally conservative: it establishes a logically closed front-end for later developments (modular generators,
CPTP-compatible dynamics, and phase structure) without introducing them here
as axioms.
Ссылка для цитирования:
Несен О. И. 2026. Canonical Emergence of the Density Operator from Normalized Probabilistic Structure. PREPRINTS.RU. https://doi.org/10.24108/preprints-3114651
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