# Quantum conditional query complexity

arXiv: https://arxiv.org/abs/1609.01600 · HTML: https://mlsanity.com/paper/1609.01600/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Sep 2016.

## Built on by (most cited first, 1 of 1)

- [Lifting uniform learners via distributional decomposition](https://mlsanity.com/paper/2303.16208/) (2023)

## Abstract (arXiv)

We define and study a new type of quantum oracle, the quantum conditional oracle, which provides oracle access to the conditional probabilities associated with an underlying distribution. Amongst other properties, we (a) obtain speed-ups over the best known quantum algorithms for identity testing, equivalence testing and uniformity testing of probability distributions; (b) study the power of these oracles for testing properties of boolean functions, and obtain an algorithm for checking whether an n-input m-output boolean function is balanced or ε-far from balanced; and (c) give a sub-linear algorithm, requiring tildeO(n3/4/ε) queries, for testing whether an n-dimensional quantum state is maximally mixed or not.