I supervise two types of undergraduate research/creative activity projects. The first type involves doing programming and web development for apps to be used in physics outreach. Detailed knowledge of physics is not required for this, but experience or interest in web development is needed. The second type are research projects. My approach to undergraduate research projects is to try to find a topic that is on the cutting edge of recent research, but is also understandable in its entirety to students who have studied the basics of quantum mechanics. I aim for students to produce research that can be published in an academic journal, rather than just presented internally in the university. This can make my projects quite challenging, but I believe this is an invaluable experience, especially for students who plan on going to graduate school. Normally I prefer to work with juniors or seniors, who will have the required background, but exceptions can be made for particularly keen students. Although I am happy to work with individual students, I believe that a small group of two or three students working on different aspects of the same problem usually works better, as you can learn a lot more from your peers than just from me.

When giving public lectures, I like to make the audience participate in games and activities that demonstrate the strange aspects of quantum theory, like nonlocality and quantum contextuality. These activities can be done with paper and pencil, but it would be better to have an online version with a web interface, and possibly smartphone apps further down the road. This project would involve coding and designing the interface for these games. This project is suitable for anyone with an interest in web development and/or web design.

One of the distinguishing features of quantum theory is that not all physical quantities can be accurately measured at once. For example, there is no way of precisely measuring both the position and momentum of a particle at the same time. A theory of incompatibility is currently being developed, which includes measuring how incompatible sets of quantum observables are. This can be applied to studies of the classical limit of quantum theory, as the accessible observables should become compatible in this limit. This project involves computing incompatibility measures for specific classes of observables and modelling how they behave in the classical limit. It is suitable for junior and senior physics or math majors and involves analytical calculations and computer modelling.

Recent experiments conducted since 2015 have demonstrated quantum nonlocality to the most rigorous possible standards in so-called “loophole free” Bell inequality tests. The aim of this project is to use the openly-available data sets from these experiments to compute measures of how nonlocal the world must be. These include the nonlocal fraction, the key rate in device independent quantum key distribution, and the amount of classical communication needed to reproduce the experimental results. These measures are well-studied theoretically, but a sophisticated statistical analysis is needed to estimate robustly them from the data. This project is suitable for anyone interested in statistics or data science, which can include freshman or sophomores who have taken appropriate classes in statistics or computer programming.

Recent results have aimed to show that the quantum state must be ontic (a state of reality) rather than epistemic (a state of information). These can be tested experimentally using overlap bounds based on quantum contextuality inequalities. The aim of this project is to show that these can be made robust to small experimental errors. If successful, we may go on to design an experimental test that could be performed in Prof. LaRue’s lab. This project will be mostly analytical, but could involve data analysis if we get as far as performing the experiment.

Quantum theory can be viewed as a generalization of probability theory in which quantum states are generalizations of classical probability distributions. Based on this idea, I have developed a notion of a quantum conditional state, which generalizes the notion of a classical probability distribution. However, unlike classical conditional probabilities, not every set of conditional states can occur as the conditionals of a joint quantum state, due to a phenomenon known as “monogamy of entanglement”. The aim of this project would be to determine the constraints for simple classes of three-qubit states. Although analytic results are possible, I expect this project to be mostly numerical.

Like every physical theory before it, quantum theory will probably eventually have to be replaced by a new and more general physical theory. Quantum theory has proved quite brittle to modifications, with many of them leading to undesired effects such as faster-than-light signalling. However, several proposed modifications to quantum theory have led to controversy. For example, a recent paper challenges the standard result that says any nonlinear modification to quantum theory must lead to faster-than-light signalling, and proponents of non hermitian quantum mechanics have claimed it violates standard results in quantum theory, such as the quantum speed limit. The goal of this project is to analyse these controversies, figure out what assumptions are being made, and determine who is right. Examples questions include:

- Does nonlinear quantum mechanics necessarily lead to faster-than-light signalling?
- Does non hermitian quantum mechanics lead to information processing advantages over standard quantum theory, or is it equivalent to standard quantum theory?
- Does the presence of a closed-timelike-curve (basically a time machine) necessarily lead to a nonlinear probability rule for quantum theory?

This project is mostly conceptual, i.e. it involves analyzing existing work and thinking hard about it rather than deriving new results.