Resource theories of multi-time processes: A window into quantum non-Markovianity

We investigate the conditions under which an uncontrollable background processes may be harnessed by an agent to perform a task that would otherwise be impossible within their operational framework. This situation can be understood from the perspective of resource theory: rather than harnessing 'useful' quantum states to perform tasks, we propose a resource theory of quantum processes across multiple points in time. Uncontrollable background processes fulfil the role of resources, and a new set of objects called superprocesses, corresponding to operationally implementable control of the system undergoing the process, constitute the transformations between them. After formally introducing a framework for deriving resource theories of multi-time processes, we present a hierarchy of examples induced by restricting quantum or classical communication within the superprocess — corresponding to a client-server scenario. The resulting nine resource theories have different notions of quantum or classical memory as the determinant of their utility. Furthermore, one of these theories has a strict correspondence between non-useful processes and those that are Markovian and, therefore, could be said to be a true 'quantum resource theory of non-Markovianity'.

Creating Superposition: The Beam Splitter

Now that we have explored qubits and the phenomenon of superposition, we can ask the question: how do we know that superposition actually happens? is the evidence that shows that a quantum particle really does exist in two different locations at this same time while in a quantum superposition? The nature of science means that experiments are constantly updating previous results, so are there other interpretations of the experimental results that can explain the data without the need for superposition? In this chapter we’ll explore the experimental evidence interpretations other than quantum superposition. Further, while a flipping coin is a simple model of a qubit, it is not very useful for building a quantum computer because it does not exhibit all of the properties of a true quantum superposition. For example, we cannot manipulate the superposition amplitudes. In this chapter, we will study some real physical examples of quantum particles in a superposition containing two states. These examples include a photon in a beam splitter and the Mach–Zehnder interferometer.

The rule of conditional probability is valid in quantum theory [Comment on Gelman & Yao's "Holes in Bayesian statistics"]

In a recent manuscript, Gelman & Yao (2020) claim that "the usual rules of conditional probability fail in the quantum realm" and that "probability theory isn't true (quantum physics)" and purport to support these statements with the example of a quantum double-slit experiment. The present comment recalls some relevant literature in quantum theory and shows that (i) Gelman & Yao's statements are false; in fact, the quantum example confirms the rules of probability theory; (ii) the particular inequality found in the quantum example can be shown to appear also in very non-quantum examples, such as drawing from an urn; thus there is nothing peculiar to quantum theory in this matter. A couple of wrong or imprecise statements about quantum theory in the cited manuscript are also corrected.

Scientific Realism without the Wave Function

Scientific realism assumes that our best scientific theories can be regarded as (approximately) true. Quantum mechanics has long been regarded as at odds with scientific realism. It is now known that this is not true. However, scientific realists usually assume that the wave function represents physical entities. Chapter 11 discusses a particular approach which makes quantum mechanics compatible with scientific realism without assuming this: matter is instead represented by some spatio-temporal entity dubbed the primitive ontology. It argues how within this framework one developsa distinctive theory-construction schema, which allows us to perform a more informed theory evaluation by analyzing the various ingredients of the approach and their inter-relations.

Simple photoreduction of carbon dioxide to formic acid and true quantum yield

There is a need to develop techniques for conversion of carbon dioxide to useful products such as formaldehyde, formic acid, methanol, and hydrocarbons.