  Any state r = (x,y,z) of a qubit, written in the Pauli basis and initialized
in the pure state r = (0,0,1), can be prepared by composing three quantum
operations: two unitary rotation gates to reach a pure state on the Bloch
sphere, followed by a depolarization gate to decrease |r|. Here we discuss the
complementary state-preparation protocol for qubits initialized at the center
of the Bloch ball, r=0, based on increasing or amplifying |r| to its desired
value, then rotating. Bloch vector amplification may or may not increase qubit
energy, but it necessarily increases purity and decreases entropy.
Amplification can be achieved with a linear Markovian CPTP channel by placing
the channel's fixed point away from r=0, making it nonunital, but the resulting
gate suffers from a critical slowing down as that fixed point is approached.
Here we consider alternative designs based on linear and nonlinear Markovian
PTP channels, which offer benefits relative to linear CPTP channels, namely
fast Bloch vector amplification without deceleration. These operations simulate
a reversal of the thermodynamic arrow of time for the qubit and would provide
striking experimental demonstrations of non-CP dynamics.
