Computing on quantum shared secrets

Abstract

A (k,n)-threshold secret-sharing scheme allows for a string to be split into n shares in such a way that any subset of at least k shares suffices to recover the secret string, but such that any subset of at most k-1 shares contains no information about the secret. Quantum secret-sharing schemes extend this idea to the sharing of quantum states. Here we propose a method of performing computation on quantum shared secrets. We introduce a (n,n)-quantum secret sharing scheme together with a set of protocols that allow quantum circuits to be evaluated on the shared secret without the need to decode the secret. We consider a multipartite setting, with each participant holding a share of the secret. We show that if there exists at least one honest participant, no group of dishonest participants can recover any information about the shared secret, independent of their deviations from the protocol.

5 pages, 2 figures, 1 table

References in corpus (4)

• Verifiable measurement-only blind quantum computing with stabilizer testing
• Quantum walks with encrypted data
• Limitations on information theoretically secure quantum homomorphic encryption
• Delegating Private Quantum Computations

Cited by in corpus (10)

• Device-independent quantum secret sharing with noise preprocessing and postselection
• Approximate reconstructability of quantum states and noisy quantum secret sharing schemes
• A quantum secret sharing scheme with verifiable function
• Quantum cryptography beyond key distribution: theory and experiment
• Quantum transfer of interacting qubits
• Quantum steering as a resource for secure tripartite Quantum State Sharing
• Computing on Quantum Shared Secrets for General Quantum Access Structures
• Quantum security computation on shared secrets
• Quantum preprocessing for information-theoretic security in two-party computation
• A framework for quantum homomorphic encryption with experimental demonstration