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Proper and improper mixed states serve as different prior beliefs for quantum state retrodiction
Mingxuan Liu, Valerio Scarani, Ge Bai
A mixed quantum state can be taken as capturing an unspecified form of ignorance; or as describing the lack of knowledge about the true pure state of the system ("proper mixture");…
Unifying Quantum Smoothing Theories with Extended Retrodiction
Mingxuan Liu, Ge Bai, Valerio Scarani
Estimating the state of an open quantum system monitored over time requires incorporating information from past measurements (filtering) and, for improved accuracy, also from futur…
A quantum entropy production operator
Ge Bai, Francesco Buscemi, Valerio Scarani
We introduce a fully quantum notion of entropy production based on the non-commutative extension of the classical log-ratio between forward and reverse processes. Given a pair of q…
Quantum Bayes' rule and Petz transpose map from the minimum change principle
Ge Bai, Francesco Buscemi, Valerio Scarani
Bayes' rule, which is routinely used to update beliefs based on new evidence, can be derived from a principle of minimum change. This principle states that updated beliefs must be…
Bayesian retrodiction of quantum supermaps
Ge Bai
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,…