Symmetry-Driven Coherence in a Symbolic Grammar for Open Quantum Systems

Krüger, Marcel

We show that symmetry–driven coherence restoration (SDCR) in open quantum systems admits a compact formulation within a symbolic grammar framework. Coherence recovery is implemented as symmetry–based restriction of admissible derivations, rather than as a modification of fundamental quantum dynamics. The construction is unitary-safe, admits explicit recovery limits to standard open-system and field-theoretic descriptions, and yields experimentally testable phase corrections.

N.A. Gromov, Костяков Игорь Владимирович, Куратов Василий Васильевич

Stanley Gudder, Richard N. Ball

Krüger, Marcel, Feeney, Don

Decoherence is a central obstacle in the control and interpretation of open quantum systems, traditionally treated as an effectively irreversible process driven by environmental coupling. In this work, we introduce a framework for symmetry-driven coherence restoration (SDCR), demonstrating that coherence loss in open systems need not be strictly monotonic when specific temporal, geometric, or algebraic symmetries are aligned within the reduced dynamics. Crucially, the framework operates entirely within standard open-quantum-system theory and does not invoke new particles, collapse mechanisms, or modifications of fundamental quantum laws. SDCR is formulated as a symmetry-selection mechanism acting on the reduced evolution of quantum systems, where dominant decohering channels are parametrically suppressed through structured symmetry alignment. This leads to partial recovery of phase coherence and to small, systematic phase corrections that preserve established scaling relations. The framework is developed consistently across Lindblad, Redfield, and influence-functional formalisms, highlighting its compatibility with both Markovian and non-Markovian dynamics. To organize coupled phase and memory channels, the theory employs octonionic and quaternionic embeddings strictly as internal algebraic tools, without attributing physical reality to additional dimensions or degrees of freedom. The phenomenological consequences of SDCR are explored in contexts where phase stability is experimentally accessible, including neutrino oscillations, matter-wave and photonic interferometry, and precision gravimetry. In these settings, SDCR predicts controlled, symmetry-correlated phase offsets that remain below existing experimental bounds yet lie within the sensitivity of current and near-future experiments. Importantly, all predicted effects vanish in the recovery limit when symmetry alignment is removed, rendering the framework explicitly falsifiable. Overall, this work presents SDCR as a conservative, testable geometric perspective on coherence control in open quantum systems. By reframing decoherence suppression as a problem of symmetry alignment rather than active feedback or new dynamics, the framework provides a unified lens through which coherence preservation and phase stability can be investigated across disparate quantum platforms.

Konstantin A. Makarov, Eduard Tsekanovskiı̆

Marcel Krüger, Don Feeney

Decoherence in open quantum systems is commonly associated with irreversible loss of phase information governed by non-Hermitian effective generators. However, the spectral structure of these generators is not invariant under all symmetry-preserving dynamical embeddings. In this work, we introduce a symmetry-driven coherence restoration (SDCR) mechanism in which structured geometric and temporal alignments induce controlled deformations of the effective Liouvillian spectrum. Within a conservative extension of open-system theory, SDCR does not modify the microscopic Hamiltonian, particle content, or fundamental interactions. Instead, it operates at the level of the reduced generator Leff, producing small but systematic redistributions of its complex eigenvalues while preserving complete positivity, trace preservation, and global unitarity of the total system. We formulate the mechanism consistently across Lindblad, Redfield, and influence-functional descriptions and show that the resulting generator deformations can be compactly organized using an internal octonionic embedding without introducing additional physical degrees of freedom. From a spectral perspective, SDCR selectively suppresses decay channels associated with specific eigenmodes rather than introducing explicit gain–loss terms, placing it naturally within the modern framework of non-Hermitian many-body dynamics. Phenomenological implications are discussed for neutrino oscillations, interferometric phase measurements, and precision gravimetry, where SDCR predicts small, symmetry-correlated phase deviations within current or near-future experimental reach. The framework is explicitly falsifiable and reduces to standard decoherence in the absence of symmetry alignment. SDCR therefore provides a conservative and testable geometric mechanism for spectral control in open quantum systems.