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Access to calls and SMS
How to get access to calls and SMS in Android and iOS in Qt?
There's no direct API for that available in Qt.
Depending on the OS, you might not even have the possibility to get that information natively.
How to do it for iOS and Android?
AFAIR, you can't for iOS. As for Android, you can check this stack overflow thread, but it might have change over time.
Why not for iOS?
That's a question you should as Apple. From a quick guess: privacy.