See also the Talks and Publications pages.

Quantum Information and Foundations of Physics

May ’24, left to right: Manuel Mekonnen (PhD student), MM, Stefan Ludescher (PhD student), Thomas Galley (postdoc), Caroline Jones (PhD student), Albert Aloy (postdoc). Not in the picture: Andrew J. P. Garner (postdoc).

We study the Foundations of Physics from an information-theoretic perspective. The main tool and inspiration is Quantum Information Theory, which we apply to a variety of questions: Can we derive the abstract formalism of quantum theory from simple principles? How can we test quantum theory against more general alternatives, under minimal assumptions? How are probabilities in arbitrary theories constrained by spatiotemporal symmetries, and what does this tell us the relation between space, time and quantum theory? What is the nature of reality and our place in it?


Aiming for complete mathematical rigor and conceptual clarity, our research touches mathematics, physics, computer science, and philosophy. Since we prove theorems with paper and pencil, our work can be broadly classified as Mathematical Physics.

Vision

Quantum theory challenges our view of the world: Bell’s Theorem proves that it is inconsistent to think that there is a single, material world with well-defined properties that just “sits there” and reveals its variables to us when we make observations, unless we give up some other important principles of physics. Our intuitions about the universe and our place in it seem to be deeply misguided. But what exactly is it that quantum physics teaches us about reality?

I believe that the most fruitful and accurate way to look at physics and its foundations is through the lens of information theory. In this view, we should not think of our world as being composed, fundamentally, of material things that move and collide, but of immaterial structure. Quantum information is our currently most accurate mathematical description of this structure. Its most fruitful and explanatorily powerful interpretation is in terms of a “catalog of probabilities”: the quantum state is the thing that gives us the probabilities of future observations. Not only does this view dissolve the measurement problem (a “collapse” is simply an update of probabilities in the light of new information), but it motivates and nourishes a particular path towards understanding the Foundations of Physics. In my own research, it has led me to pursue, for example, the following research directions:

  • Reconstructions of Quantum Theory. Quantum theory is one of our most successful physical theories, but its standard textbook formulation is mysterious. For example, why are states described by complex vectors in a Hilbert space, and why do observables correspond to self-adjoint operators? In the last few years, my colleagues and I have shown (based on pioneering work by Lucien Hardy) that the formalism of quantum theory can be reconstructed from simple information-theoretic principles, without presupposing any of the usual mathematical machinery. This is conceptually similar to the derivation of the Lorentz transformations from the principles and relativity and the constancy of the speed of light.
    Note that this formalism starts without assuming that there is something like an operator algebra, or amplitudes, or any other ingredients of the usual mathematical formalism. Instead, these properties are rigorously and non-trivially derived from the information-theoretic principles.
  • Resource-Theoretic Approach to Thermodynamics. In this approach, thermodynamics is not seen as a theory about, say, the statistical properties of the evolution of a large ensemble of gas particles, but as a theory that describes the constraints faced by an agent who plays a “game” against nature. Namely, if an experimenter is constrained by reversible time evolution and energy conservation, then what kinds of transformations can they perform on their physical system? It turns out that this “resource-theoretic” approach can be used to put the known laws of thermodynamics on rigorous mathematical and conceptual footing. For example, according to this view, it is immediately obvious that the information held by an agent impacts its ability to, say, extract energy, which makes insights like Landauer’s Principle much less surprising. Moreover, this approach leads to proofs of the standard laws of thermodynamics, and also to surprising refinements as they apply to “small” quantum systems without going to the thermodynamic limit.
  • Testing Quantum Theory. The above reasoning suggests that quantum theory is only one possible probabilistic theory among many others. This view leads to new proposals for experimental tests of quantum theory (and, indirectly, to progress on understanding quantum information): design experiments that probe its probabilistic structure, but that do so in a theory-agnostic way without presupposing any particular alternative. An example approach can be found in this paper, where we have recently suggested a scheme for experimentally testing quantum theory that can — as a by-product — also be used to certify the nonclassicality of physical systems. Putting this into actual practice is the content of a current project funded by the FWF.
  • The Structure of Physics. Furthermore, this particular way of looking at quantum theory allows us to examine some of the logical structure of physics. For example, we can examine whether and how other probabilistic theories “fit into space and time” in the same way as quantum theory does. This research reveals that spacetime places severe constraints on the probabilistic theory that applies to our world, revealing exciting insights into the structural architecture of our physical world. I believe that this may also shed some light on the problem of quantum gravity: if we think that there is a fundamental theory (QG or something else) that, in some limit, reduces to general relativity and quantum theory as emergent approximations, then the structure of these two theories should reflect this interplay by showing that they “fit together” in unusual and surprising ways. And this is indeed what is shown in some of this research.

I see quantum theory as just one of several indicators that our view of reality and our place in it is fundamentally incomplete. In order to arrive at a view that is less wrong, an amalgam of theoretical physics, mathematics, computer science and philosophy is needed. In doing so, however, I believe that we should ask different types of questions than the ones that are usually asked, and that we should wonder about different things than we usually do. Instead of asking “what is the correct Lagrangian of the universe, and how can we quantize it?”, we should ask: why Lagrangians in the first place, and why quantum theory? Instead of wondering about the notions of causality and time asymmetry in our physical world, we should be surprised and concerned that our world fulfills a physical version of the Church-Turing thesis. Instead of asking what factual configuration of stuff underlies our quantum world, we should reconsider our prejudices as to why there should be a world in the first place, and ask what exactly we think that this means and whether there are other options. Modern computer science, the rationality community and science fiction are perhaps better guides towards progress than the questions that have typically been discussed in the philosophy of science. At the very least, they remind us how narrow-minded and wrong our views may be, including everything that you are reading right now.

This sort of thinking has led me towards somewhat idiosyncratic research directions. For example, it has led us to speculate that the linearity of vectors and tensors in our physical world (why should there be such structure?) is fundamentally grounded in the linearity of probabilities. More significantly, it has led me to suggest an approach (“Algorithmic Idealism“) in which not an external world, but a technical notion of the “first person” (sort of the “self”, but not consciousness) is fundamental. This is a reaction to some enigmas in the foundations of physics, cosmology, and philosophy, including the computer simulation of agents. From a more technical point of view, it is a reaction to an observation (also described in different terminology by others) that Caroline Jones and I call “Restriction A“: that our physical theories cannot give us probability distributions for the observations of all agents, suggesting some fundamental “fragmentalism” in the foundations of the physical world.

All that being sad, I am still a mathematical physicist by heart: I believe that, ultimately, the core of all claims lies in the mathematical structures and not in the stories that we decide to tell ourselves about them. After all, no matter how much we err today, our mathematical theorems will still stand tomorrow.

Topics and Projects

A colorful overview of some of our topics can be found on my homepage’s front page. See also the Publications and Talks pages.

Here is a partial list of current and previous research topics that our group has worked on. The more detailed descriptions (see links) are hosted on my group’s IQOQI website.

  • Reconstructions of Quantum Theory. Our group has contributed one of the first complete and fully rigorous reconstructions of QT from simple principles. This research has several aims: a better understanding of QT; proposals for natural modifications of QT that are potentially relevant in physics and computer science; devising experimental tests of QT; or understanding the structural relation between space, time and quantum theory. More details here.
  • Quantum Thermodynamics. We have worked on the resource-theoretic approach to thermodynamics, have discovered the phenomenon of “correlated catalysis“, and we have contributed significant results on the thermalization of closed quantum system. Furthermore, we have contributed a rigorous proof of “thermalization from entanglement” for translation-invariant models and have proven concentration of measure for the mean energy ensemble. More here.
  • Algorithmic Idealism. I have proposed an approach to the foundations of physics in which not an external world, but a mathematical notion of the first person (sort of the “self”, but not consciousness) is fundamental. The goal is not philosophical contemplation, but a unified framework that yields concrete predictions for puzzling thought experiments about physics, agents, computer simulation, and cosmology. More on this website.
  • Quantum Reference Frames. It has been argued that all physical quantities are described relative to some reference frame. But since all physical systems are quantum, reference frames must be, too. Our group has contributed several rigorous results to the recent wave of interest on these “internal QRFs”, such as a quantitative version of the Page-Wootters formalism, an axiomatic treatment of QRFs for finite Abelian groups, an algebraic resolution of the apparent “paradox of the third particle”, and an elaboration of the “perspective-neutral” approach. More details here.
  • Generalized Probabilistic Theories. Similarly as Euclidean and Minkowski spacetime are just two of many possible theories of geometry, quantum theory is just one of many probabilistic theories (and so is classical probability theory). Our group has contributed a multitude of results on GPTs, for example that bit symmetry implies self-duality, decoupling theorems, or a classification of all unrestricted GPTs that are embeddable into quantum theory. More here.
  • Classical and Quantum Algorithmic Information Theory. Kolmogorov complexity and AIT describe concrete single instances of physical systems (“data”), in contrast to standard information theory that deals with the statistical properties of all possible realizations of a system. In my PhD thesis, I have proven several results that are essential to make sense of earlier proposals of a quantum version of Kolmogorov complexity, such as its invariance with respect to the choice of (strongly universal) quantum Turing machine, its agreement with the classical version on classical bit strings, or quantum notions of prefix-freedom. Moreover, I have worked on effective complexity and shown that it is impossible in general to introduce a machine-independent notion of (classical) algorithmic probability.
  • Generalized Noncontextuality. Spekkens’ notion of generalized noncontextuality is perhaps our conceptually clearest notion of nonclassicality in the absence of constraints arising from causal structure. With Andy Garner, I have introduced a generalized notion of generalized noncontextuality that allows us not only to ask whether classical hidden variables are a plausible explanation of our laboratory data, but also whether quantum theory provides such an explanation (we would strongly expect that it does). This should lead us to novel protocols for testing quantum theory in a fully device- and causality-independent way. My group is currently working on an FWF-funded project (see below) that will use these results to certify nonclassicality in large quantum systems.

Finally, here is a list of recent (after 2021) third-party-funded projects. For earlier projects, please see my CV page.

Generalized Contextuality in Large Quantum Systems

Quantum theory promises technological applications that would be impossible within classical physics: faster computation, more accurate metrology, or the generation of provably secure random numbers. However, to make this work, we first need to test whether our devices are really quantum and work as desired a task called certification. This is not only relevant for technology, but also for fundamental physics: given some large physical system, such as a Bose-Einstein condensate, how can we prove that its properties cannot be explained by classical physics? In other words, how can we certify its nonclassicality? In this project, we will develop a new method to do so, both theoretically (via mathematical proofs and conceptual argumentation) and experimentally (with concrete data supplied by colleagues at ETH Zurich). […] Read more.

Black-Box Quantum Information Under Spacetime Symmetries

Quantum theory has not only revolutionized our understanding of physics, but it has also led to a multitude of technological applications in information theory. For example, quantum physics admits unconditionally secure cryptography or the generation of provably random numbers. […] Previous research has focused on black boxes with abstract inputs and outputs, like abstract bits (zeros and ones) as commonly used in information theory. But in many actual experiments, the inputs and outputs are not abstract, but concrete spatiotemporal quantities such as the spatial direction of a magnetic field, the duration of a pulse, or the angle of a polarizer. The goal of this project is to theoretically analyze the foundations and applications of such spatiotemporal black boxes.[…] Read more.

Local Operations on Quantum Fields

The notion of locality is one of the most important concepts of science. In non-relativistic quantum mechanics, it is usually built into the formalism by demanding that composite systems compose with the tensor product.
In Quantum Field Theory (QFT), the rules of the game change: all operations act on the same Hilbert space, and space-like separated operations are required to commute (microcausality). However, as observed by Sorkin, microcausality alone does not exclude faster-than-light communication in experiments with more than two separate parties. In this regard, QFT is an incomplete physical theory: it still lacks a mathematical description of the most general operations that an experimenter can conduct within a finite space and in a finite time. […]
In this project, we aim to provide an explicit mathematical formulation of local operations for QFT and QG. […]

Joint project with Časlav Brukner, Borivoje Dakić, and Miguel Navascués.

Mathematical Models of Idealism and Dualism: an Adversarial Collaboration

The rationalist blog Slate Star Codex defines an “adversarial collaboration” as “an effort by two people with opposing opinions on a topic to collaborate on a summary of the evidence. The question on which the two applicants disagree is this: Does consciousness play a directly relevant role in quantum theory, in particular in the context of the measurement problem? Kelvin McQueen believes that the answer could well be “yes”: consciousness may be responsible for wave function collapse, in a way that can be described by explicit mathematical models. Markus Müller believes that the answer is “no”: quantum states represent propensities of an agent’s future records, and collapse is probabilistic update. […]
Joint project with Kelvin McQueen.

Former group members

  • Marius Krumm (PhD student), now Postdoc at the University of Innsbruck.
  • Philipp Höhn (postdoc), now Assistant Professor at Okinawa Institute of Science and Technology.
  • Mark Francis Rogers (pre-university research student), now at the University of Manchester.
  • Michele Pastena (PhD student), now Project Engineer with Safetec GmbH.
  • Jakob Scharlau (Master student), now with dida Machine Learning.
  • Michael Cuffaro (postdoc), now Alexander von Humboldt Fellow and external member of the Munich Center for Mathematical Philosophy.
  • Adam Koberinski (Graduate Student Assistant), now Postdoctoral Fellow at the Rotman Institute of Philosophy.
  • Jonathon Riddell (undergraduate “work study” student), now Research Fellow at the University of Birmingham.
  • Nicole Yunger Halpern (PSI Master Student, Perimeter Institute for Theoretical Physics), now NIST physicist and Adjunct Assistant Professor of Physics and IPST at the University of Maryland. Rob Spekkens and I taught Nicole the resource-theoretic approach to thermodynamics, and now she’s leading a Quantum Steampunk Laboratory. 🙂
  • Emily Adlam (PSI Summer Student, Perimeter Institute), now Assistant Professor of Philosophy at Chapman University.
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