I receive a "could not sign in" error after upgrade to iOS 11.0
Try switching networks. 

If you were using Wi-Fi try another Wi-Fi or switch over to mobile data by disabling Wi-Fi. If you were using your mobile data, try using Wi-Fi.

Often times that helps me out.

If those dont work then you have some options:


Restart device
Reset network settings (if you can get to them)
If resetting device and settings didn't work, check for an iCloud backup or iTunes backup (iCloud preferred). And then erase &amp; restore the iPhone without the backup. If you can sign in with no problem then erase, restore and bring your backup up.


If you can't sign in after the 1st erase and restore without the backup then, call AppleCare and let us know everything that was done and make sure to mention that the restore was done, but it hasn't fixed the issue.