Conditioning through indifference in quantum mechanics

TL;DR

This paper develops a general rule for updating beliefs about a quantum system's state after measurements, based on the interplay of desirability, coherence, and indifference, extending to multiple outcomes.

Contribution

It introduces a novel conditioning rule in quantum mechanics derived from desirability, coherence, and indifference principles, generalizing existing methods.

Findings

Derived a general rule for quantum state conditioning.

Extended the rule to multiple measurement outcomes.

Provides a unified framework for quantum belief updates.

Abstract

We can learn (more) about the state a quantum system is in through measurements. We look at how to describe the uncertainty about a quantum system's state conditional on executing such measurements. We show that by exploiting the interplay between desirability, coherence and indifference, a general rule for conditioning can be derived. We then apply this rule to conditioning on measurement outcomes, and show how it generalises to conditioning on a set of measurement outcomes.