Finding a causal model for a set of classical variables is now awell-established task---but what about the quantum equivalent? Even the notionof a quantum causal model is controversial. Here, we present a causal discoveryalgorithm for quantum systems. The input to the algorithm is a process matrixdescribing correlations between quantum events. Its output consists ofdifferent levels of information about the underlying causal model. Ouralgorithm determines whether the process is causally ordered by grouping theevents into causally-ordered non-signaling sets. It detects if all relevantcommon causes are included in the process, which we label Markovian, oralternatively if some causal relations are mediated through some externalmemory. For a Markovian process, it outputs a causal model, namely the causalrelations and the corresponding mechanisms, represented as quantum states andchannels. Our algorithm provides a first step towards more general methods forquantum causal discovery.
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