A core tenet of Bayesian epistemology is that rational agents update by Bayesian conditionalization. Accuracy arguments in favor of this norm are well-known. Meanwhile, in the setting of quantum probability and quantum state estimation, multiple updating rules have been proposed, all of which look prima facie like analogues of Bayesian conditionalization. These include Luders conditionalization, retrodiction, and Bayesian mean estimation (BME). In this paper, we present expected-accuracy and accuracy-dominance arguments for Luders and BME, which we show are complementary rules. Retrodiction, on the other hand, is shown to be accuracy-dominated, at least on many measures.

Orthodox quantum theory tells us that properties of quantum systems are represented by self-adjoint operators, and that two properties are incompatible just in case their respective operators do not commute. We present a puzzle for this orthodoxy, pinpointing the exact assumptions at play. Our solution to the puzzle specifically challenges the assumption that non-commuting operators represent incompatible properties. Instead, they represent incompatible levels of specification of determinates for a single determinable. This solution yields insight into the nature of so-called quantum indeterminacy and demonstrates a new and fruitful application of the determinable-determinate relation in quantum theory.

The popular metaphysical view that concrete objects are grounded in their ultimate parts is often motivated by appeals to realist interpretations of contemporary physics. This paper argues that an examination of mainstream interpretations of quantum mechanics undercuts such atomist claims. First, mereological atomism is only plausible in conjunction with Bohmian mechanics. Second, on either an endurantist or perdurantist theory of time, atomism exacerbates Bohmianism’s existing tensions with serious Lorentz invariance in a way that undermines the realist appeal of both views. Bohmians should therefore resist atomism, leaving atomists somewhat physically homeless.