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arXiv:2205.10057 · Physical Review Research

Symmetry-induced decoherence-free subspaces

Jonathan Dubois, Ulf Saalmann, Jan Michael Rost

Published Jan 12, 2023• 10 citations
arXivHTMLPDF

Abstract

Preservation of coherence is a fundamental, yet subtle, phenomenon in open systems.We uncover its relation to symmetries respected by the system Hamiltonian and its coupling to the environment.We discriminate between local and global classes of decoherence-free subspaces for many-body systems through the introduction of "ghost variables".The latter are orthogonal to the symmetry and the coupling to the environment depends solely on them.Constructing them is facilitated in classical phase space and can be transferred to quantum mechanics through the equivalent role that Poisson and Lie algebras play for symmetries in classical and quantum mechanics, respectively.Examples are given for an interacting spin system.

DOI
10.1103/physrevresearch.5.l012003

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Preservation of coherence is a fundamental, yet subtle, phenomenon in open systems.We uncover its relation to symmetries respected by the system Hamiltonian and its coupling to the environment.We discriminate between local and global classes of decoherence-free subspaces for many-body systems through the introduction of "ghost variables".The latter are orthogonal to the symmetry and the coupling to the environment depends solely on them.Constructing them is facilitated in classical phase space and can be transferred to quantum mechanics through the equivalent role that Poisson and Lie algebras play for symmetries in classical and quantum mechanics, respectively.Examples are given for an interacting spin system.
Coherence in an open quantum system is degraded through its interaction with a bath. This decoherence can be avoided by restricting the dynamics of the system to special decoherence-free subspaces. These subspaces are usually constructed under the assumption of spatially symmetric system-bath coupling. Here we show that decoherence-free subspaces may appear without spatial symmetry. Instead, we consider a model of system-bath interactions in which to first order only multiple-qubit coupling to the bath is present, with single-qubit system-bath coupling absent. We derive necessary and sufficient conditions for the appearance of decoherence-free states in this model, and give a number of examples. In a sequel paper we show how to perform universal and fault tolerant quantum computation on the decoherence-free subspaces considered in this paper.
We investigate the fate of coherence in the dynamical evolution of symmetry protected quantum systems. Under the formalism of system plus bath for open quantum systems, antiunitary symmetries exhibit significant differences from the unitary ones in protecting initial coherence. Specifically, taking advantage of the Lindblad master equation, we find that a pure state in the symmetry protected degenerate subspace will be decoherent even though both the system Hamiltonian and system-environment interaction respect the same antiunitary symmetry. In contrast, the coherence will persist when the protecting symmetry is unitary. We provide an elaborate classification table to illustrate what kinds of symmetry combinations are able to preserve the coherence of the initial state, which is confirmed in several concrete models of single spin-3/23/23/2 systems. It can also be applied to the Haldane phase in interacting topological systems. Our results could be helpful in exploring possible experimental realization of stable time-reversal symmetric topological states.
Symmetry principles have played a crucial role in the development of modern physics and underpin our most fundamental theories of nature. The present thesis is concerned with the analysis of symmetries in the context of quantum information theory. Whenever a quantum mechanical system interacts with its environment it is subjected to decoherence, a process that is typically irreversible and most generally treated abstractly using the concept of quantum operations. If there is an underlying symmetry principle, additional structures emerge. The central question we address is, What are the consequences of global or local gauge symmetry on the structure of many-body quantum processes?This leads us to a diagrammatic framework of decomposing quantum operations into terms that respond to the symmetry principle in particular ways and respect the causal structures involved. We present two core applications. First, we address the interplay between irreversibility and repeatable use of coherent resources under symmetry constraints. Second, we give an information-theoretic perspective on gauging globally symmetric dynamics to a local symmetry applicable even in the presence of irreversibility and thus it goes beyond the usual Lagrangian formulation. Finally, we analyse the departure from conservation laws under symmetric dynamics subject to decoherence.
Quantum superpositions can be used for parallel information processing, but only if protected against decoherence. A two-particle four-state system may have two-dimensional subspaces that are partially or completely decoherence-free, e.g., the symmetric triplet state as an example of the former, the anti-symmetric singlet state of the latter. By extension, a multiparticle system that in the laboratory basis is plagued by decoherence may in some other basis exhibit the symmetries that yield such decoherence-free subspaces (DFS's). Fully-interacting many-fermion spin 1/2 networks may be mathematically transformed to a more tractable many-to-one (or -to-some) variant. This paper applies such a transformation to a hypothetical network of boson-like operators and then argues that a fully-interacting particle number-preserving network of bosons plus fermions with supersymmetric degrees of freedom may be more plausibly exploited so as to contain DFS's. Physical systems that in some basis are inherently anti-symmetric are already known to be useful for quantum information processing. Supersymmetric systems may be likewise.
Decoherence is a fundamental limitation in open quantum systems, yet recent developments indicate that coherence loss need not be strictly irreversible. In this work, we introduce a symmetrydriven coherence restoration (SDCR) framework in which structured temporal and geometric symmetries suppress dominant decohering channels without modifying fundamental quantum dynamics. The framework is formulated within a conservative extension of open-system theory and does not introduce new particles, interactions, or collapse mechanisms. Instead, SDCR emerges from symmetry alignment in an extended dynamical structure, leading to small but systematic phase corrections while preserving standard scaling relations. We provide a unified description across Lindblad, Redfield, and influence-functional formulations and demonstrate that SDCR admits a compact algebraic embedding using octonionic structures as an internal organizational tool. Phenomenological implications are discussed for neutrino oscillations, interferometry, and precision gravimetry, where SDCR predicts experimentally accessible signatures within current and near-future sensitivities. The framework is explicitly falsifiable and reduces to standard decoherence in the absence of symmetry alignment. SDCR thus provides a conservative and testable geometric perspective on coherence control in open quantum systems.