Abstract

In the classical world, upon receiving new evidence, beliefs are (well… should be) updated according to the Bayes’ rule. The quantum analog of this rule is not straightforward and has been the subject of several discussions. Recently, we have found the quantum Bayes’ rule that emerges from a “minimum change principle”, that is the idea that one should update one’s beliefs in the least disruptive way. In many cases, it coincides with the Petz map, one of the most popular previously proposed candidates; in some situations, it is a map that nobody had anticipated. I shall also discuss how the quantum belief should not be restricted to the state, but comprises any information we may have about its preparation. Based on this observation, we have been able to unify various proposals for the task of “smoothing” in a single framework.

About the speaker

Valerio Scarani is Principal Investigator (currently serving as Deputy Director) at the Centre for Quantum Technologies, and Professor at the Department of Physics, National University of Singapore. His research is in theoretical quantum information science, with works in quantum cryptography, Bell nonlocality and other topics.