Definition
Quantum cryptography uses quantum-mechanical effects to perform cryptographic tasks. The flagship application is Quantum Key Distribution (QKD), which lets two parties exchange a shared key over a fibre-optic or free-space link in a way that any eavesdropping disturbs the quantum state and is detectable. QKD is a real, deployed technology in some banking and government links, but it requires special hardware and dedicated channels.
Quantum vs Post-Quantum
These two terms are often confused. Quantum cryptography uses quantum physics to do cryptography. Post-quantum cryptography uses ordinary classical computers but with new algorithms designed to resist attack from future large-scale quantum computers. The everyday concern for VPNs is post-quantum cryptography — software updates that protect today's traffic against the quantum computers of tomorrow. QKD is currently irrelevant to consumer VPNs because it requires dedicated quantum-capable hardware on both ends.
Status
QKD has been demonstrated over hundreds of kilometres of fibre and via satellite, and a small number of commercial products exist. It is unlikely to be a consumer technology in the foreseeable future. Post-quantum cryptography, by contrast, is already being rolled out: TLS 1.3 supports hybrid Kyber key exchange, and forward-looking VPN providers have begun integrating PQ algorithms into their handshakes.