Verifiable Hybrid Secret Sharing With Few Qubits

Abstract

We consider the task of sharing a secret quantum state in a quantum network in a verifiable way. We propose a protocol that achieves this task, while reducing the number of required qubits, as compared to the existing protocols. To achieve this, we combine classical encryption of the quantum secret with an existing verifiable quantum secret sharing scheme based on Calderbank-Shor-Steane quantum error correcting codes. In this way we obtain a verifiable hybrid secret sharing scheme for sharing qubits, which combines the benefits of quantum and classical schemes. Our scheme does not reveal any information to any group of less than half of the $n$ nodes participating in the protocol. Moreover, for sharing a one-qubit state each node needs a quantum memory to store $n$ single-qubit shares, and requires a workspace of at most $3n$ qubits in total to verify the quantum secret. Importantly, in our scheme an individual share is encoded in a single qubit, as opposed to previous schemes requiring $\Omega (\log n)$ qubits per share. Furthermore, we define a ramp verifiable hybrid scheme. We give explicit examples of various verifiable hybrid schemes based on existing quantum error correcting codes.

arXiv comment12 + 5 pages, 3 figures

References in corpus (24)

• Quantum secret sharing
• Good Quantum Error-Correcting Codes Exist
• How to share a quantum secret
• Multiple Particle Interference and Quantum Error Correction
• A Theory of Quantum Error-Correcting Codes
• Efficient Multi-Party Quantum Secret Sharing Schemes
• On the Theory of Quantum Secret Sharing
• Graph States for Quantum Secret Sharing
• Quantum codes on a lattice with boundary
• Trading classical and quantum computational resources
• Authentication of Quantum Messages
• Tapering off qubits to simulate fermionic Hamiltonians
• Experimental demonstration of graph-state quantum secret sharing
• Generalized Quantum Secret Sharing
• Lowering qubit requirements for quantum simulations of fermionic systems
• Secure Multiparty Quantum Computation with (Only) a Strict Honest Majority
• Fault-tolerant quantum computing with color codes
• Quantum Secret Sharing Schemes and Reversibility of Quantum Operations
• Optimizing qubit resources for quantum chemistry simulations in second quantization on a quantum computer
• Reducing the quantum communication cost of quantum secret sharing
• Generalized Semi-Quantum Secret Sharing Schemes
• On the equivalence between sharing quantum and classical secrets, and error correction
• Private Quantum Channels and the Cost of Randomizing Quantum Information
• Multi-party Quantum Computation

Cited by in corpus (4)

• Secure multi-party quantum computation with few qubits
• Exploring strong locality : Quantum state discrimination regime and beyond
• Classifying locally distinguishable sets: No activation across bipartitions
• Secure multi-party quantum computation protocol for quantum circuits: the exploitation of triply-even quantum error-correcting codes