If what I assume is correct, you need to mimick what facebook/linkedin/twitter have and create something similar to:
OAuth ("The OAuth 2.0 Authorization Framework", RFC 6749)
What this means is that the client applications need to obtain the required keys to be allowed to access users/user-data from the single login.
The issue with this type of scenario is that it can become quite complex (so hopefully you're working with a team).
Some of the reasons it will become complex:
- Building out the internal infrastructure to deal with Authorization and the passing of data to client applications
- Security of the login feature (your service will be handling all logins and will need to at least have strong encryption, etc.)
- Maintaining an API/documentation that provides all the required information for other developers to use the API to access users/user-data
Another suggestion I might consider is to create a "thin" login functionality that lives below all other applications (basically, it is a single application that is structured in a way where all other applications are built on top of it (it sounds similar to what an API is, but it is different in the sense that the login and client application are more strongly coupled).
The main point you should realize from this is that any solution you find will be "somewhat" complex to implement (based on your exp. and how many are in your team, etc.).