  The interaction of a quantum system with its environment limits qubit
coherence times and restricts its utility in quantum information processing
applications. In this Letter, we show that the decoherence of a coupled qubit
system can be minimized, or even eliminated by exploiting the quantum coherence
of the bath itself. We investigate the dephasing in a system of two spatially
separated, electronically decoupled qubits, with direct or mediated coupling,
interacting with a shared bath. For illustration we treat F\"orster or
cavity-mediated coupling between semiconductor quantum dots interacting with
acoustic phonons. Using the rigorous method of Trotter's decomposition with
cumulant expansion, we demonstrate a reduction in the dephasing rates at
specific distances. This control is a coherent effect of the shared bath and is
absent for independent baths. It can be understood in terms of phonon-assisted
transitions between the entangled qubit states of the coupled system.
