Symmetry-induced decoherence-free subspaces

TL;DR

This paper explores how symmetries in many-body quantum systems can create decoherence-free subspaces, using classical phase space concepts and introducing 'ghost variables' to distinguish local and global cases.

Contribution

It introduces the concept of ghost variables to differentiate local and global decoherence-free subspaces and links classical and quantum symmetry structures for their construction.

Findings

Decoherence-free subspaces relate to system symmetries.

Ghost variables are orthogonal to symmetry and environment coupling.

Application demonstrated in an interacting spin system.

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 does not depend 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.