Characterization-free classification and identification of the environment between two quantum players

TL;DR

This paper presents a device-independent protocol for classifying the causal order of quantum channels between two players, using input-output statistics without prior knowledge, and demonstrates its effectiveness experimentally.

Contribution

It introduces a characterization-free, device-independent method for identifying the causal structure of quantum channels between two parties, validated through experimental implementation.

Findings

Protocol reliably distinguishes causal strategies with minimal resources.

The method is proven to be both necessary and sufficient for classification.

Experimental results confirm the protocol's robustness and accuracy.

Abstract

Classifying the causal structure of quantum channels is essential for verifying quantum networks and certifying quantum resources. We introduce a characterization-free protocol enabling two isolated players, Alice and Bob, to classify and identify the definite-order strategy adopted by an unknown environment mediating their channels. Without assuming knowledge of their devices or the environment, the players infer the causal order solely from input-output statistics by testing Markovian conditions that we prove are necessary and sufficient for each strategy class. Remarkably, we prove that even with a minimal random channel consisting of two-outcome POVMs and two-state preparations, the protocol retains full performance with probability one. We experimentally demonstrate the protocol on an optical platform, reliably distinguishing between several strategies. Our results provide a strong and robust tool for causal inference in quantum networks.