Pseudorandom States, Non-Cloning Theorems and Quantum Money
This work addresses the foundational challenge of creating secure quantum cryptographic primitives, specifically for quantum money, representing a novel theoretical advancement rather than an incremental improvement.
The paper tackles the problem of constructing pseudorandom quantum states by proposing their concept and providing efficient constructions based on quantum-secure one-way functions, with the non-cloning theorem ensuring security against copying. As a result, it proves that such states naturally yield a private-key quantum money scheme, enabling secure quantum currency.
We propose the concept of pseudorandom states and study their constructions, properties, and applications. Under the assumption that quantum-secure one-way functions exist, we present concrete and efficient constructions of pseudorandom states. The non-cloning theorem plays a central role in our study---it motivates the proper definition and characterizes one of the important properties of pseudorandom quantum states. Namely, there is no efficient quantum algorithm that can create more copies of the state from a given number of pseudorandom states. As the main application, we prove that any family of pseudorandom states naturally gives rise to a private-key quantum money scheme.