I would not leave a pre-teen home alone for even an hour. There's SO much that could happen, God forbid. Especially if someone came to the door, if she has access to internet, if someone called, if she happened to tell a friend and the friend happened to tell someone... if it became known to a predator that she's alone..... if there was a fire, if there was a "simple" random burglary (someone not even knowing she's there) which is common in neighborhoods where MOST of the residents work, leaving most homes empty during regular 8 - 5 work week hours....
and then, as you mentioned, what kind of quality will she have to her day? soaps? game shows? video games? friends over?
My pre-teen would be told that they have a say in most things that go on in the house that affect them, but as for this situation, she'd simply have to trust you and go to summper camp, or "hang out with" an elderly neighbor (good for HER and good for the elderly person, or some other supervised situation. An 11 year old doesnt have the life experience and such to be able to care for herself 4 - 8 hours a day.... in my opinion.
She needs stimulation, communication, and socialization at that age, for that length of period that you're away.
And, God forbid, if anything at all happened to her while alone, you'd never forgive yourself.