How did the Emperor know that Alia was Paul's sister?

Question

In Dune how did the Emperor know that Alia was Paul's sister? No-one knew Jessica was pregnant, let alone had survived the Harkonnen attack on House Atreides. The Surdaukar that were captured and release by Muad'dib and the Fremen only knew about Paul, and Alia would have easily passed for a normal Fremen child.

Answer 1

Alia told the Sardaukar her identity when she "allowed" herself to be captured, and the Sardaukar presumably told the Emperor when they gave their account of the battle.

“Unfortunately,” the Emperor said, “I only sent in five troop carriers with a light attack force to pick up prisoners for questioning. We barely got away with three prisoners and one carrier. Mind you, Baron, my Sardaukar were almost overwhelmed by a force composed mostly of women, children, and old men. This child here was in command of one of the attacking groups.”
“You see, Your Majesty!” the Baron said. “You see how they are!”
“I allowed myself to be captured,” the child said. “I did not want to face my brother and have to tell him that his son had been killed.”

The Sardaukar claimed the child Alia was in command of a number of Fremen fighters and recognised that Alia was an important enough prisoner to be taken aboard the (very few) craft that managed to escape the battle.