First, there is a small misinterpretation because quantum cryptography does not in any way serve to break the cryptographic mechanisms currently in use. Quantum cryptography provides an alternative, which is unquestionably secure, as has been demonstrated.
That said, conventional cryptography and quantum cryptography can be used not against each other, but together toward the same goal, which is the protection of privacy and confidentiality.
The danger to conventional cryptography is the quantum computer, not quantum cryptography. We hope that no one knows how to build it, or at least that there isn't one that's already working. However, since the 1990s, we have known how it could be used to break cryptographic systems underlying Internet security or pseudo‑security today.