Bad Qubits — Learn Quantum by Doing

Multiple choice

Two initial states of an open quantum system are compared using their trace distance D(rho1, rho2), which measures how distinguishable they are. Under any Markovian (CP-divisible) evolution, how can this distinguishability change over time, and what does a temporary INCREASE signal?

It can only decrease monotonically; a temporary increase signals information flowing back from the bath to the system, the hallmark of non-Markovian dynamics
It oscillates periodically under all Markovian evolution; a constant value signals non-Markovian dynamics
It can only increase monotonically; a temporary decrease signals non-Markovian dynamics
It stays exactly constant; any change at all signals non-Markovian dynamics