Trusted center verification model and classical channel remote state preparation

• URL: http://arxiv.org/abs/2008.05033v2
• Date: Tue, 1 Sep 2020 02:12:11 GMT
• Title: Trusted center verification model and classical channel remote state preparation
• Authors: Tomoyuki Morimae, Yuki Takeuchi
• Abstract summary: The classical channel remote state preparation (ccRSP) is an important two-party primitive in quantum cryptography. We consider a general verification protocol where the verifier or the trusted center first sends quantum states to the prover, and then the prover and the verifier exchange a constant round of classical messages. We show that the first quantum message transmission cannot be replaced with an (even approximate) ccRSP protocol while keeping the information-theoretical soundness unless BQP is contained in AM.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The classical channel remote state preparation (ccRSP) is an important two-party primitive in quantum cryptography. Alice (classical polynomial-time) and Bob (quantum polynomial-time) exchange polynomial rounds of classical messages, and Bob finally gets random single-qubit states while Alice finally gets classical descriptions of the states. In [T. Morimae, arXiv:2003.10712], an information-theoretically-sound non-interactive protocol for the verification of quantum computing was proposed. The verifier of the protocol is classical, but the trusted center is assumed that sends random single-qubit states to the prover and their classical descriptions to the verifier. If the trusted center can be replaced with a ccRSP protocol while keeping the information-theoretical soundness, an information-theoretically-sound classical verification of quantum computing is possible, which solves the long-standing open problem. In this paper, we show that it is not the case unless BQP is contained in MA. We also consider a general verification protocol where the verifier or the trusted center first sends quantum states to the prover, and then the prover and the verifier exchange a constant round of classical messages. We show that the first quantum message transmission cannot be replaced with an (even approximate) ccRSP protocol while keeping the information-theoretical soundness unless BQP is contained in AM. We finally study the verification with the computational soundness. We show that if a ccRSP protocol satisfies a certain condition even against any quantum polynomial-time malicious prover, the replacement of the trusted center with the ccRSP protocol realizes a computationally-sound classical verification of quantum computing. The condition is weaker than the verifiability of the ccRSP.

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