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Pseudorandom States, Non-Cloning Theorems and Quantum Money
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.Comment: 20 page
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