Long-term research interests

Modelling agents as physical systems in quantum theory and beyond

Naturally, we would like physical theories to be consistent with available experimental data. We acquire this data through subjective experiences, while at the same time knowing ourselves to be physical systems, which should also be modelled by the theory. Therefore, a base requirement for a physical theory is that it contain a mapping from subjective to outsider views of experiences.

For example, several interpretations of quantum mechanics allow us to model the observer’s memory as a quantum system, which may become entangled with the system measured in a reversible manner, while from the observer’s perspective a collapse has occurred. In thermodynamics, looking explicitly at Maxwell’s demon‘s memory (and the need to erase it) allowed us to understand an apparent contradiction of the Second Law.

In many proposals for new physical theories, however, the explicit modelling of observers as physical systems is lacking: this is the case of quantum gravity, string theory and other attempts to unify general relativity and quantum mechanics.

I am interested in modelling agents as physical systems within different theories, from memories to processors, and simulate the processes of performing observations, combining information and making predictions. We can then study the limitations that these theories place on the rationality of such agents.

Logic, knowledge and security in quantum networks

While standard quantum algorithms at the moment end with a measurement and classical post-processing of information, we would like to study the possibilities of large networks of quantum information-processing components which relay quantum information to each other in a coherent way; this is part of the promise of a quantum internet.

As we work towards reliable quantum networks with many nodes, we must develop the tools to analyze quantum cryptography and communication scenarios with many parties, and in particular to track flows of knowledge in such settings. Current quantum cryptography approaches can model complex situations, but are still built upon a basis of intuitive classical logic, which allows us to make inferences of the sort “I know that Eve does not know the secret key, and I know that the secret key is required in order to decode the message, therefore I know that Eve cannot know the message.” While this seems natural and even trivial, Frauchiger and Renner have shown that applying a similarly simple reasoning to a particular quantum experiment can lead to contradictions.

I am interested in investigating the consequences of this and similar experiments for logic in general, and quantum networks in particular. We have already found that modal logic — which is the most successful way to formalize simple principles of reasoning — breaks down in quantum settings. The consequences trickle down to quantum communication and cryptography theory: if we cannot apply usual logic to settings where different parties may be modelled by quantum memories, then the range of applicability of current proofs may be more limited than we expect.

Foundations of quantum complexity theory

Most approaches within quantum complexity theory take the circuit model (based on a quantum Turing machine) as the basic framework to determine what can be computed efficiently by exploring the quantum effects of matter. Efficiency in the circuit model is measured in terms of number of qubits and elementary gates needed to solve a given task. Operations or algorithms that are efficient to implement on a quantum circuit are assumed to be easy to implement in a laboratory and vice-versa, up to polynomial overheads. This is the basis for the quantum complexity-theoretic Church-Turing thesis, which claims quantum circuits can efficiently simulate any physical model of computation. As a consequence, efforts to build a quantum computer tend to follow the circuit model, where unitary gates are applied in sequence.

Note however that the intuition behind the quantum circuit model comes from a restricted simplification of quantum physics to abstract information-theoretical concepts. Therefore, it may miss out on dynamic quantum phenomena, which are not easily represented as a sequence of gates in a circuit. For example, we could ask about the implications to complexity theory if we could prepare superpositions of large masses that led to a superposition of space-time manifolds and causal structures. More generally, I believe that quantum foundations research can inform the basis for a more comprehensive framework for quantum complexity theory, which will reflect more faithfully which processes can be efficiently implemented in Nature and in a quantum computer.

The overall goals of this research programme are two-fold: we want to explore exotic quantum phenomena for information-processing tasks, and to generalize the quantum circuit model, and therefore quantum complexity theory, so that its notion of efficiency matches what can be easily implemented in Nature and in physics laboratories. We will investigate whether the advantage of a physical implementation over the circuit model can only ever be polynomial, or if alternative computation models which explore the wealth of quantum causality can give us an exponential speedup.

Publications and pre-prints

For an updated list of publications, see my Google Scholar profile, ORCiD 0000-0002-2445-2701 or arXiv list.

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