Foundations of Quantum Programming

5.3.3 Persistence Probability

The aim of this subsection is to study another kind of reachability of quantum Markov chains, namely persistence. Intuitively, persistence means that a desired condition is always satisfied from a certain point of time. As pointed out in the last subsection, we can focus our attention on ${\mathcal{E}}_{\infty }(\mathcal{H})$ because ${\mathcal{E}}_{\infty }{(\mathcal{H})}^{\perp }$ is a transient subspace.

Definition 5.3.3

Let $\mathcal{C}=\langle \mathcal{H},\mathcal{E}\rangle$ be a quantum Markov chain and X a subspace of ${\mathcal{E}}_{\infty }(\mathcal{H})$. Then ...