Quantum Probability Estimation for Randomness with Quantum Side Information

Understand

We develop a quantum version of the probability estimation framework [arXiv:1709.06159] for randomness generation with quantum side information.

• We show that most of the properties of probability estimation hold for quantum probability estimation (QPE).
• This includes asymptotic optimality at constant error and randomness expansion with logarithmic input entropy.
• QPE is implemented by constructing model-dependent quantum estimation factors (QEFs), which yield statistical confidence upper bounds on data-conditional normalized R\'enyi powers.