Symmetry-induced decoherence-free subspaces

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.

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• Quantum non-demolition measurement of an electron spin qubit through its low-energy many-body spin environment
• Relaxation Control of Open Quantum Systems
• Dark-state photonic entanglement filters
• Emergence of the Gibbs ensemble as a steady state in Lindbladian dynamics