11. Given a cube $A B C D-A_{1} B_{1} C_{1} D_{1}$ with edge length 1, the symmetric points of point $A$ about the lines $A_{1} C$ and $B D_{1}$ are points $P$ and $Q$, respectively. Then the distance between points $P$ and $Q$ is ( ).
(A) $\frac{2 \sqrt{2}}{3}$
(B) $\frac{3 \sqrt{3}}{2}$
(C) $\frac{3 \sqrt{2}}{4}$
(D) $\frac{4 \sqrt{2}}{3}$