The simplest way to accomplish what you want is to make the backup process run as an administrator. Administrators have full access to all users' profile folders, but they must run elevated for this access control entry to apply.
If you can't run the backup elevated, make the backup user an administrator, log on as it, and try to navigate into other users' profile folders. Windows Explorer will inform you that access is denied, but it will give you a button that permanently grants the current user access to that folder. After that's done, the backup user will be able to access that other user's profile even without elevation.
Information on how to replicate the effect of the Backup Operators group follows below the line.
Much of what makes the Backup Operators group special is that, by default, it is granted a handful of privileges:
SeBackupPrivilege, "back up files and directories"
SeRestorePrivilege, "restore files and directories"
SeShutdownPrivilege, "shut down the system"
SeBatchLogonRight, "log on as a batch job"
Privileges can be assigned using the User Rights Assignment section of the Local Security Policy tool,
secpol.msc. That tool might not exist on non-Pro editions of Windows, though. To adjust privileges on other editions, you can use the NTRights utility from the Windows Server 2003 Resource Kit. Despite the name, that kit can be installed on any modern version of Windows. You can use NTRights to grant a privilege by opening an administrative command prompt and running a command like this:
ntrights -u YourBackupUser +r SeSomePrivilege
YourBackupUser with the SAM account name of the user/group who should be able to back up and restore — the SAM account names are listed in the output of
net user or
net localgroup (ignore the asterisk before the group name). Replace
SeSomePrivilege with the ID of the privilege to grant. If you want to revoke a privilege later, run the same command but with
-r instead of
Note, though, that only specially written software will be able to take advantage of these privileges. Even when granted, privileges must be enabled per process before they take effect, then the program must call special read/write APIs that bypass security checks. These privileges are also insufficient for creating shadow copies; to do that, a process must be running as a member of the Administrators group — even membership in the real Backup Operators group isn't enough for that.