# Pseudorandom States, Non-Cloning Theorems and Quantum Money

arXiv: https://arxiv.org/abs/1711.00385 · HTML: https://mlsanity.com/paper/1711.00385/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Nov 2017.

## Built on by (most cited first, 3 of 3)

- [How to Construct Random Unitaries](https://mlsanity.com/paper/2410.10116/) (2024)
- [Quantum Solutions to the Privacy vs. Utility Tradeoff](https://mlsanity.com/paper/2307.03118/) (2023)
- [Estimating the randomness of quantum circuit ensembles up to 50 qubits](https://mlsanity.com/paper/2205.09900/) (2022)

## Abstract (arXiv)

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.