Quantum Causal Inference with Extremely Light Touch

TL;DR

This paper introduces a quantum causal inference method that uses minimal measurements to determine causal structures in bipartite quantum systems over time, leveraging properties of the pseudo-density matrix.

Contribution

It provides a novel protocol for quantum causal inference based solely on light-touch measurements, capable of distinguishing causal directions and correlations without requiring full state tomography.

Findings

The protocol can determine causal structures with coarse measurements.

Negativity in the PDM indicates signaling between subsystems.

The method works even with decohering channels and does not require quantum coherence.

Abstract

We give a causal inference scheme using quantum observations alone for a case with both temporal and spatial correlations: a bipartite quantum system with measurements at two times. The protocol determines compatibility with 5 causal structures distinguished by the direction of causal influence and whether there are initial correlations. We derive and exploit a closed-form expression for the space-time pseudo-density matrix (PDM) for many times and qubits. This PDM can be determined by light-touch coarse-grained measurements alone. We prove that if there is no signalling between two subsystems, the reduced state of the PDM cannot have negativity, regardless of initial spatial correlations. In addition, the protocol exploits the time asymmetry of the PDM to determine the temporal order. The protocol succeeds for a state with coherence undergoing a fully decohering channel. Thus coherence in the channel is not necessary for the quantum advantage of causal inference from observations alone.