Fig. 1. Influence of noise factor p and memory factor μ on fidelity.(a) $\left|\psi \right.〉$ = $\sqrt[]{\mathrm{0.5}}$$\left|\mathrm{0}\right.〉$ +$\sqrt[]{\mathrm{0.5}}$$\left|\mathrm{1}\right.〉$ ; (b) $\left|\psi \right.〉$ = $\sqrt[]{\mathrm{0.3}}$$\left|\mathrm{0}\right.〉$ +$\sqrt[]{\mathrm{0.7}}$$\left|\mathrm{1}\right.〉$ ; (c) $\left|\psi \right.〉$ = $\sqrt[]{\mathrm{0.8}}$$\left|\mathrm{0}\right.〉$ +$\sqrt[]{\mathrm{0.2}}$$\left|\mathrm{1}\right.〉$

Fig. 2. Influence of weak measurement strength p${}_{\mathrm{w}}$(a) $\mu =\mathrm{0}$; (b) $\mu =\mathrm{0.5}$; (c) $\mu =\mathrm{1}$and amplitude damping noise factor p on fidelity.