Non-Destructive Zero-Knowledge Proofs on Quantum States, and Multi-Party Generation of Authorized Hidden GHZ States
This work addresses foundational challenges in quantum cryptography by enabling secure, efficient verification and distribution of quantum states, with potential applications in quantum anonymous transmission and secret sharing.
The paper introduces the first non-interactive zero-knowledge proofs for quantum languages, enabling non-destructive verification of quantum states with a single message, and improves remote state preparation protocols by creating multi-qubit states from a single superposition, generalizing these to multi-party settings for secure GHZ state distribution.
We propose the first generalization of the famous Non-Interactive Zero-Knowledge (NIZK) proofs to quantum languages (NIZKoQS) and we provide a protocol to prove advanced properties on a received quantum state non-destructively and non-interactively (a single message being sent from the prover to the verifier). In our second orthogonal contribution, we improve the costly Remote State Preparation protocols [CCKW18,CCKW19,GV19] that can classically fake a quantum channel (this is at the heart of our NIZKoQS protocol) by showing how to create a multi-qubits state from a single superposition. Finally, we generalize these results to a multi-party setting and prove that multiple parties can anonymously distribute a GHZ state in such a way that only participants knowing a secret credential can share this state, which could have applications to quantum anonymous transmission, quantum secret sharing, quantum onion routing and more.