# Quantum oracles give an advantage for identifying classical counterfactuals

arXiv: https://arxiv.org/abs/2512.13692 · HTML: https://mlsanity.com/paper/2512.13692/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 42 references that are in the map.
- First posted on arXiv 15 Dec 2025.

## Builds on (most cited first, 10 of 10)

- [D'ARTAGNAN: Counterfactual Video Generation](https://mlsanity.com/paper/2206.01651/) (2022)
- [Stochastic Causal Programming for Bounding Treatment Effects](https://mlsanity.com/paper/2202.10806/) (2022)
- [Estimating Categorical Counterfactuals via Deep Twin Networks](https://mlsanity.com/paper/2109.01904/) (2021)
- [Estimating long-term causal effects from short-term experiments and long-term observational data with unobserved confounding](https://mlsanity.com/paper/2302.10625/) (2023)
- [Contrastive representations of high-dimensional, structured treatments](https://mlsanity.com/paper/2411.19245/) (2024)
- [Non-parametric identifiability and sensitivity analysis of synthetic control models](https://mlsanity.com/paper/2301.07656/) (2023)
- [Spillover Detection for Donor Selection in Synthetic Control Models](https://mlsanity.com/paper/2406.11399/) (2024)
- [Algorithmic Recourse in Partially and Fully Confounded Settings Through Bounding Counterfactual Effects](https://mlsanity.com/paper/2106.11849/) (2021)
- [Nature versus nurture in galaxy formation: the effect of environment on star formation with causal machine learning](https://mlsanity.com/paper/2412.02439/) (2024)
- [Local Interference: Removing Interference Bias in Semi-Parametric Causal Models](https://mlsanity.com/paper/2503.18756/) (2025)

## Abstract (arXiv)

We show that quantum oracles provide an advantage over classical oracles for answering classical counterfactual questions in causal models, or equivalently, for identifying unknown causal parameters such as distributions over functional dependences. In structural causal models with discrete classical variables, observational data and even ideal interventions generally fail to answer all counterfactual questions, since different causal parameters can reproduce the same observational and interventional data while disagreeing on counterfactuals. Using a simple binary example, we demonstrate that if the classical variables of interest are encoded in quantum systems and the causal dependence among them is encoded in a quantum oracle, coherently querying the oracle enables the identification of all causal parameters -- hence all classical counterfactuals. We generalize this to arbitrary finite cardinalities and prove that coherent probing 1) allows the identification of all two-way joint counterfactuals p(Y_x=y, Y_{x'}=y'), which is not possible with any number of queries to a classical oracle, and 2) provides tighter bounds on higher-order multi-way counterfactuals than with a classical oracle. This work can also be viewed as an extension to traditional quantum oracle problems such as Deutsch--Jozsa to identifying more causal parameters beyond just, e.g., whether a function is constant or balanced. Finally, we raise the question of whether this quantum advantage relies on uniquely non-classical features like contextuality. We provide some evidence against this by showing that in the binary case, oracles in some classically-explainable theories like Spekkens' toy theory also give rise to a counterfactual identifiability advantage over strictly classical oracles.