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) $\frac{4 \sqrt{2}}{3}$
11.A.

Establish a spatial rectangular coordinate system, with $D(0,0,0), A(1,0,0), A_{1}(1,0,1), C(0,1,0), B(1,1,0), D_{1}(0,0,1)$. Let $P(x, y, z)$, and the midpoint of $A P$ be $M\left(\frac{x+1}{2}, \frac{y}{2}, \frac{z}{2}\right)$.
From $A P \cdot A_{1} C=0, M C / / A_{1} C$, we get
Similarly, $Q\left(\frac{1}{3}, \frac{4}{3}, \frac{2}{3}\right)$.
Thus, $|P Q|=\frac{2 \sqrt{2}}{3}$.