Xuwei Ou
Quantum Transfer Entropy of Incoherent Channels and Causal Interpretation.
Rel. Davide Girolami. Politecnico di Torino, Master of science program in Quantum Engineering, 2025
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Abstract
Transfer entropy plays an important role in causal inference and causal discovery in time series analysis. As an information-theoretic measure, transfer entropy can detect nonlinear causal structures without any prior model assumptions. The transfer-entropy-based causal analysis scenario thus has a broader range of applications than the model-based methods like Granger causality tests. This study generalizes the definition of transfer entropy to time-parameterized quantum processes. We define a basis-dependent operational measure of one-way information flow through incoherent channels, called quantum transfer entropy. Quantum transfer entropy provides a new characteristic of quantum channels. A nonzero quantum transfer entropy indicates the directed causal influence from the source to the target.
In addition, we study controlled-Z channels and find that the quantum transfer entropy is a linear function of the total information of the control qubit—including both classical Shannon information and coherence in a given reference basis —thus providing an operational interpretation of information flow through quantum control channels
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