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arXiv:2610.30616

On the Structure of Quantum Finite-Level Systems: Decoherence-Free Subsystems, Quantum Nondemolition Variables, and Back-Action-Evading Measurements

Jia Gu, Guofeng Zhang, Ian R. Petersen

quant-pheess.SYSubmitted Oct 22, 2026• Announced Oct 23, 2026• 0 citations

Abstract

The purpose of this paper is to conduct a comprehensive structural analysis of quantum finite-level systems in the Heisenberg picture, where the evolution of system observables is modeled by bilinear quantum stochastic differential equations (QSDEs). Firstly, real coordinate transformations that preserve commutation and anticommutation relations are characterized, and relative admissibility between different orthonormal Hermitian bases is formulated. Secondly, strongly aligned subspaces are introduced, based on which decoherence-free subsystems (DFSs) are constructed in general orthonormal Hermitian basis as well as the generalized Gell-Mann basis. Thirdly, conditions for the existence of quantum nondemolition (QND) variables are given in terms of both linear systems theory and spectral separation by output-signal observables. Finally, a sufficient condition for quantum back-action-evading (BAE) measurements is established. A four-qubit nearest-neighbor Heisenberg chain with collective dephasing illustrates these structural properties of quantum finite-level systems.

Comments: 16 pages, comments are welcome

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