Bayesian retrodiction of quantum supermaps

• URL: http://arxiv.org/abs/2408.07885v2
• Date: Tue, 27 Aug 2024 05:12:02 GMT
• Title: Bayesian retrodiction of quantum supermaps
• Authors: Ge Bai,
• Abstract summary: We study a higher-order generalization of the quantum Bayes' rule by considering a quantum process undergoing a quantum supermap. For a few families of initial beliefs, we show that a similar unification is possible -- the rules to update the belief of quantum channels can be implemented via a "reverse" quantum supermap.
• Score: 0.27195102129094995
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Petz map has been established as a quantum version of the Bayes' rule. It unifies the conceptual belief update rule of a quantum state observed after a forward quantum process, and the operational reverse process that brings the final state to a recovered state equal to the updated belief, counteracting the forward process. Here, we study a higher-order generalization of the quantum Bayes' rule by considering a quantum process undergoing a quantum supermap. For a few families of initial beliefs, we show that a similar unification is possible -- the rules to update the belief of quantum channels can be implemented via a "reverse" quantum supermap, which we call the retrodiction supermap, allowing for applications such as error correction in quantum cloud computing. Analytical solutions are provided for those families, while a recipe for arbitrary initial beliefs is yet to be found.

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