Quantum Shell Games: How to Classically Delegate the Preparation of Authenticated Quantum States
John Hunter McKnight

Abstract:
We propose novel protocols for verifiable, classically instructed remote state preparation. Our “Shell Game” protocols require constantly many rounds of communication to prepare an arbitrary number of qubits, and the prepared qubits can optionally be authenticated using a trap code. In the Shell Game, a classical client and quantum server use a new cryptographic resource called a “magic box” to perform secret CNOT and SWAP operations that encode, permute, and encrypt a quantum state held by the server. The keys to this encoding/encryption are private to the client. The client tests the server’s honesty by asking the server to measure some of the prepared state and evaluating the consistency of the outcomes against the honest state. The remaining, unmeasured state is the quantum output of the protocol.
We give a practical construction of magic boxes using Mahadev’s secret-CNOT gadget in the quantum honest-but-curious setting. We prove the Shell Game protocols secure against adversaries in this limited setting. We include a case study on the security of magic boxes against adversaries as a first step toward proving security of the Shell Game against active adversaries.