Cooperative control of dissipative qubits: steering along the fastest dissipative contraction

In the control of dissipative quantum systems, the slow relaxation modes usually set the ultimate manipulation timescale. We show that this bottleneck can be bypassed when dissipation itself is used as the engine of the transfer. For a qubit with non-unital, anisotropic Bloch relaxation characterized by the ratio κ=T 1/T 2>1, coherent control can only rotate the Bloch vector, whereas the bath alone can change its length. The fastest transfer between two thermal states therefore consists in steering the Bloch vector, at every instant, along the direction in which the bath contracts it most rapidly. This direction is obtained in closed form and lies slightly beyond the equatorial plane. With strong pulses, the resulting minimum transfer time is a fraction of T 2, instead of several T 1 for passive relaxation. With bounded fields, the Pontryagin maximum principle yields a bang--singular--bang synthesis whose singular arc is precisely this fastest-contraction direction, and the minimum time exceeds its strong-pulse limit by a correction inversely proportional to the field amplitude. We also determine the full time--energy Pareto front: moderate accelerations require little energy, and the time optimum lies at its steep, high-energy end. Off-axis targets are treated within the same framework; their only additional benefit is a shorter final rotation. These results apply directly to magnetic-resonance spins, nitrogen-vacancy centers and superconducting qubits, all of which operate deep in the strong-pulse regime.