SeBackupPrivilege | Use SE_BACKUP_NAME/SeBackupPrivilege to access objects | Continuous Backup library

Take a look at the CreateRestrictedToken and CreateProcessAsUser functions.

The first allows you to create an access token that is a restricted version of an existing token (most likely obtained via GetCurrentProcessToken or GetCurrentThreadToken and the second allows you to create a process using a specified access token (rather than the current process' existing primary access token). Note that if you use a thread token you may need to use DuplicateHandle to convert an impersonation token into a primary access token.

The cause of this is missing permission on the target process. For testing the required permission can be viewed with Process Explorer and right clicking target process and selecting Properties then Security tab and selecting Permissions button, you can add the required permission Process Query Information Allow for the user account the process calling OpenProcess is running as. Permission can also be denied due to process mandatory integrity control i.e. Medium level integrity process cannot access High integrity process. Even if the user account is added the correct permission but you do not have access due to mandatory integrity control you will get access denied.

In code this can be achieved by modifying the ACLs of the object as documented here

Here is a PowerShell script I wrote for testing different scenarios, such as adding the permission required.

See my comment above: