California has some of the strictest privacy regulations in the U.S., and unlike in many other states, the right to privacy is spelled out .

"Typically, we've been a bellwether state," said LeBlanc. "We were the first state to pass a 'do not call' list and the first to pass a law requiring data breaches are notified to consumers."

Formation of the unit puts California ahead of other states when it comes to online privacy, said Justin Brookman, director of consumer privacy at the Center for Democracy and Technology. Brookman worked in the New York Attorney General's office from 2004 to 2009.

"One advantage the states have is they can move more quickly on issues [than the U.S. Federal Trade Commission]," he said.

The FTC will generally take time to consider issues in detail, and that can mean it is more likely to get things right, but the states have the advantage when it comes to awarding large fines, he said.