Author: Jeet Mozumdar
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DOI (Zenodo): https://doi.org/10.5281/zenodo.20687402
ORCID: https://orcid.org/0009-0005-4371-2416
We introduce a tensor-network channel framework for compressed quantum dynamics on operator subsystems associated with variational many-body manifolds. Starting from a tensor-network manifold, we construct manifold-induced Heisenberg channels acting on observables and study the resulting sequential dynamics via their Schr\"odinger duals. The central mathematical result is a compression-stability statement establishing controlled approximation of sequential manifold-induced evolution, yielding a well-defined operator-system description of compressed dynamics with quantitatively bounded leakage. To connect this operator-algebraic structure with tensor-network geometry, we formulate a representability assumption asserting that intrinsic states on the compressed operator subsystem admit tensor-network representatives of bounded bond dimension. Under this assumption, tensor-network geometric structure emerges as a consequence of compressed operator dynamics rather than being imposed a priori as a variational ansatz. All geometric statements are therefore conditional on this representability assumption and do not follow from the operator-algebraic framework alone. In this setting, we establish a graph-cut mutual-information bound for representable states and introduce a geometric correlation-capacity functional determined by bond dimension and network architecture. These results provide quantitative constraints on correlation propagation within the compressed subsystem and relate information flow directly to tensor-network geometry. The framework separates a rigorous operator-algebraic layer—governing compressed observable dynamics and stability under sequential projection—from a conditional geometric layer arising under representability. This separation isolates a mathematically precise core independent of tensor-network structure while identifying the representability problem as the key bridge to geometry. From a physical perspective, tensor-network geometry becomes a dynamical constraint on information propagation and correlation capacity in compressed quantum systems. Illustrative examples involving matrix-product-state manifolds and comparisons across tensor-network architectures demonstrate how graph geometry controls representable correlation scaling. The resulting picture establishes a unified connection between compressed quantum dynamics, operator systems, tensor-network geometry, and quantum information theory, with geometry emerging from operator-algebraic compression under representability.ntum systems.
@article{mozumdar2026,
author = {Jeet Mozumdar},
title = {Compressed Quantum Dynamics and Emergent Tensor-Network Geometry in Operator Systems},
year = {2026},
doi = {10.5281/zenodo.20687401},
publisher = {Zenodo}
}
Last updated: 14 June 2026
Compressed quantum dynamics, manifold-induced channels, completely positive maps, operator algebras, tensor networks, representability assumption, graph-cut bounds, quantum information theory, many-body quantum systems
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