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

TL;DR

This paper introduces a novel non-destructive, non-interactive zero-knowledge proof system for quantum states, improves remote state preparation protocols, and enables multi-party anonymous GHZ state distribution with potential quantum communication applications.

Contribution

It generalizes NIZK proofs to quantum states, enhances remote state preparation efficiency, and develops multi-party quantum secret sharing with anonymity features.

Findings

First quantum NIZKoQS protocol demonstrated

Improved remote state preparation from single superposition

Multi-party anonymous GHZ state distribution achieved

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.