Symmetry-induced decoherence-free subspaces

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.

Automated summary

The preservation of coherence in open systems is a fundamental phenomenon related to the symmetries of the system Hamiltonian and its coupling to the environment. By introducing ghost variables, we distinguish between local and global decoherence-free subspaces for many-body systems, where the coupling to the environment depends solely on these variables. The construction of these variables is facilitated in classical phase space and can be transferred to quantum mechanics using the equivalence of Poisson and Lie algebras for symmetries in classical and quantum mechanics. Examples are provided for an interacting spin system.