The most well known and developed application of quantum cryptography is
quantum key distribution, which is the process of using quantum communication to establish a shared key between two parties (Alice and Bob, for example) without a third party (Eve) learning anything about that key, even if Eve can eavesdrop on all communication between Alice and Bob. If Eve tries to learn information about the key being established, key establishment will fail causing Alice and Bob to notice. Once the key is established, it is then typically used for
encrypted communication using classical techniques. For instance, the exchanged key could be used as for
symmetric cryptography.
The security of quantum key distribution can be proven mathematically without imposing any restrictions on the abilities of an eavesdropper, something not possible with classical key distribution. This is usually described as "unconditional security", although there are some minimal assumptions required, including that the laws of quantum mechanics apply and that Alice and Bob are able to authenticate each other, i.e. Eve should not be able to impersonate Alice or Bob as otherwise a
man-in-the-middle attack would be possible.
One aspect of quantum key distribution is that it is secure against quantum computers. Its strength does not depend on mathematical complexity, like
post-quantum cryptography, but on physical principles.
https://en.wikipedia.org/wiki/Quantum_cryptography
