Quantum Trapdoor Functions From Classical One-Way Functions

The existence of trapdoor functions is considered to be a qualitatively stronger assumption than the existence of one-way functions. In this talk, I will introduce the notion of a “quantum trapdoor function”. This is an efficiently computable unitary with trapdoor-like properties that takes as input a classical string (together with a “public” quantum state), and outputs a quantum state. I will show that a trapdoor quantum function can be constructed from any (quantum-secure) one-way function.