Control-Induced Decoherence-Free Manifolds

TL;DR

This paper introduces a dynamic approach to creating and maintaining decoherence-free subspaces in open quantum systems through quantum control, leveraging topological and algebraic structures to preserve quantum coherence.

Contribution

It proposes a novel time-varying decoherence-free subspace framework that utilizes quantum control to sustain quantum coherence in open systems.

Findings

Defines a time-varying DFS with unitarily evolving sub-density matrices

Characterizes the DFS using topological and algebraic methods

Shows the DFS forms a complex vector bundle over a real-analytic manifold

Abstract

Quantum coherence of open quantum systems is usually compromised because of the interaction with the ambient environment. A "decoherence-free subspace" (DFS) of the system Hilbert space is defined where the evolution remains unitary. In the absence of a priori existence of such subspaces, it seems natural that utilizing quantum control may help generate and/or retain a DFS. Here, we introduce a time-varying DFS wherein the system's density matrix has a unitarily evolving sub-density corresponding to some given set of its eigenvalues (which we aim to preserve). This subspace is characterized from both topological and algebraic perspectives. In particular, we show that this DFS admits a complex vector bundle structure over a real-analytic manifold (the decoherence-free manifold).