Only an administrator can enable postmortem debugging.
However, postmortem debugging is enabled for the entire system, not just for one user. Thus, after it has been enabled, any application crash will activate the debugger that has been chosen -- even if the current user does not have administrative privileges.
Also, a postmortem debugger inherits the same privileges as the application that crashed. Thus, if a Windows service such as CSRSS and LSASS crashes, the debugger will have very high-level privileges.
You should take this into account when choosing to enable postmortem debugging.