We develop an operator algebraic generalization of the Yoshida-Kitaev information recovery protocol that applies to von Neumann algebras of arbitrary type. The construction is based on finite-index inclusions, with the Jones basic construction and canonical endomorphisms providing the central algebraic tools. Unlike the finite-dimensional qubit description, the infinite-dimensional theory exhibits new structural phenomena that play an essential role in information recovery. In particular, the diary information is represented non-locally by a choice of Pimsner-Popa basis associated with the inclusion. Exploiting the Temperley-Lieb relations satisfied by the Jones projections, we introduce an algebraic notion of computational complexity and show that it is naturally measured by the Jones-Kosaki index. For irreducible depth-two inclusions, we demonstrate that the information transfer is implemented by an algebraic Fourier transform. Finally, we discuss a potential spacetime interpretation of the construction, including the emergence of an island algebra in terms of (non-)isometric embeddings and an operator algebraic realization of black hole complementarity.
We develop a Hopf-algebraic theory of the graph coefficients arising in the quantum Magnus expansion. At the classical level, the graph expansion is governed by directed trees, whereas its quantum counterpart involves loop graphs, multiple edges, and different types of edge data. We introduce a contraction Hopf algebra...
Li Guo, Joon-Hwi Kim, Jung-Wook Kim et al.· 1 citation
We introduce the Quantum Information Space at Infinity (Quinfinity) $\mathcal{Q}_\infty$ as the inverse limit of the symbolic Quantum $N$-Spaces $\mathcal{Q}_N$, identified with the complete local real algebra of formal power series under the adic topology. The pure state pro-variety is formalized as the inverse limit...
We develop a cohomological framework for entanglement entropy that unifies perspectives from information theory, operator algebras, and noncommutative geometry. Starting from the information-theoretic characterization of entropy as a 1-cocycle, we show how this structure generalizes to the quantum setting through Hochs...
Lie algebras describe how control Hamiltonians combine in closed quantum systems. In open Markovian systems, however, dissipation introduces irreversible directions that the Lie algebra alone does not retain. A dynamical Lie wedge preserves this information as a convex cone of locally admissible generators. The classic...
PauLie is introduced, an open-source framework that decides this isomorphism type for DLAs generated by arbitrary Pauli strings, building on the anticommutation-graph reduction of Aguilar et al.
Oxana Shaya, Konstantin Golovkin, Mainak Roy et al.· 0 citations
Every finite-dimensional real or complex Lie algebra has a largest solvable ideal, its radical. In the compact dynamical Lie algebra (DLA) of a closed quantum system, this radical is the center; projecting onto it isolates directions that commute with the supplied algebra. With sparse Lie-bracket data and a known spect...
Yi-Bin Wang· 0 citations
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