I want to make an application that has some views for information display. If I install my app on my iPhone then it should display the info. If I then install that app on my iPad then the app should recognize the device and display the info related to my account.
Is there any way to find the single user of two devices without the user's iTunes credentials, or is it possible to generate a key that can identify the common user of both devices?
No, currently there is no way to associate multiple devices to a single user owning those devices given the information you've provided.
However, if you added, "the information I want to display in the views, pertains to the same user account in Game Center for both devices", then you could use the player's identifier from Game Kit API.