Non-Destructive Zero-Knowledge Proofs on Quantum States, and Multi-Party Generation of Authorized Hidden GHZ States

• URL: http://arxiv.org/abs/2104.04742v3
• Date: Tue, 17 Jan 2023 12:36:47 GMT
• Title: Non-Destructive Zero-Knowledge Proofs on Quantum States, and Multi-Party Generation of Authorized Hidden GHZ States
• Authors: L\'eo Colisson and Fr\'ed\'eric Grosshans and Elham Kashefi
• Abstract summary: We provide a protocol to prove advanced properties on a received quantum state non-destructively and non-interactively. We show how to create a multi-qubits state from a single superposition. We generalize these results to a multi-party setting and prove that multiple parties can anonymously distribute a GHZ state.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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