I am a Research Group Leader at the Institute for Quantum Optics and Quantum Information (IQOQI) Vienna, a Lecturer at the University of Vienna, and a Visiting Fellow at the Perimeter Institute for Theoretical Physics in Waterloo, Canada. I am also an Associate Faculty member of the Rotman Institute of Philosophy.

My research is motivated by Wheeler’s “It From Bit” paradigm: to understand the foundations of physics, we have to take an information-theoretic perspective. I have worked on deriving quantum theory from simple principles, on the resource-theoretic approach to thermodynamics, and I have suggested a view (“Algorithmic Idealism”) in which not the external world, but a mathematical notion of the first person is fundamental (more topics and details below).

My research has led to several awards, including a Canada Research Chair, the Birkhoff-von Neumann prize, and ÖAW’s Best Paper Award. I am extremely grateful for the opportunity to work with a group of talented and enthusiastic young researchers at IQOQI Vienna.

## Summer 2024

- Thinking with Manuel Mekonnen about quantum reference frames, compositionality, locality and gauge theories in our Quantum Science Austria project “Local operations on quantum fields”.
- Our FWF project “Generalized contextuality in large quantum systems” continues, with Albert Aloy, Caroline Jones, Thomas Galley, and our colleagues at ETH Zurich and ICTQT Gdańsk.
- Continuing our FWF project on “Black-box quantum information under spacetime symmetries” and the Adversarial Collaboration with philosopher Kelvin McQueen on Algorithmic Idealism.
- To
**contact**me, you can write to markus.mueller (at-symbol) oeaw.ac.at.

## Recent and upcoming

- July 2024:
**Podcast**by Ding Jia with Matt Leifer and me, on interpretations of quantum theory and the nature of reality. Episodes: 1 (Matt), 2 (me), 3.1, 3.2, 3.3 (our debate). - 26 Nov 2024: Public talk at Urania Graz. “Quantenphysik und Realität: was wir wissen, was wir vermuten, und worüber wir uns wundern”.

## Selected Talks and Podcasts

A list of all talks (with links to videos and slides) can be found on my Talks page.

**Testing quantum theory by generalizing noncontextuality**

**Podcast with Karl Friston on my Algorithmic Idealism approach**

Why do I propose this approach, how is it done, and what can it predict? I am grateful to Karl Friston and the Philosophy Babble team for the opportunity to discuss this with them.

**Algorithmic idealism – what if the world is not fundamental?**

**Operational interpretation of entropy and free energy without the thermodynamic limit**

See this PRX paper: In the resource-theoretic approach to thermodynamics, the Helmholtz free energy attains a surprising operational interpretation without any thermodynamic limit, for single small quantum systems.

**Quantum theory and Jordan algebras from simple principles**

**Theory-independent randomness generation with spacetime symmetries**

We demonstrate that important predictions of quantum theory can be derived from the structure of space, without assuming the quantum formalism. This allows us to propose a theory-independent scheme for generating certified randomness.

## Selected Papers

All papers including Open Access links can be found on my Publications page.

Thinking twice inside the box — is Wigner’s friend really quantum?

We argue that the gist of Wigner’s friend is a feature we call “Restriction A”, and that it underlies a much broader class of (non-quantum) enigmas in the foundations of physics and philosophy, including cosmology’s Boltzmann brain problem.

Correlating Thermal Machines and the Second Law at the Nanoscale

I show that the Helmholtz free energy F has a physical interpretation without any averaging or thermodynamic limit: it determines the (im)possibility of state transitions of *single*, small quantum systems if the heat engine is allowed to become correlated or entangled with the work medium while preserving its own state.

A derivation of quantum theory from physical requirements

We derive the Hilbert space formalism of quantum theory from a few simple information-theoretic principles, without presupposing any of its mathematical machinery (such as operators or complex numbers). This solved a longstanding open problem in the field.

Quantum reference frame transformations as symmetries and the paradox of the 3rd particle

We give an axiomatic definition of QRF transformations for finite discrete translations. This resolves an apparent paradox from the literature with an algebraic treatment of how system composition should be understood under quantum symmetries.

The quantum bit from relativity of simultaneity on an interferometer

A simple thought experiment that shows a fundamental relation between spacetime and quantum theory: the qubit Bloch ball must be either 1-, 2-, 3- or 5-dimensional (i.e. classical, or quantum over the reals, complex numbers or quaternions) because of relativity of simultaneity.

An operational approach to spacetime symmetries: Lorentz transformations from quantum communication

Usually, we think of spacetime symmetries as fundamental and implement them unitarily in quantum theory. Here we suggest that this reasoning can be reversed: communicating quantum laboratories must be related by an element of the Lorentz group merely due to the structure of quantum theory.

The black hole information problem beyond quantum theory

We derive the Page curve (and the Hayden-Preskill results) for general probabilistic theories beyond quantum theory, rigorously and axiomatically. Black hole evaporation turns out to depend on an interference parameter r, where r=2 for QT.

Testing Quantum Theory by Generalizing Noncontextuality

If Nature is fundamentally quantum, which effective statistics (for example, classical probabilities) can we plausibly expect to see in the lab? We give a complete answer to this question and use this to propose a novel experimental test of quantum theory.

The measurement postulates of quantum mechanics are operationally redundant

If unitary quantum mechanics leads to probabilities somehow, then these must be described by the Born rule. We give a particularly careful und rigorous proof of this, without hidden assumptions, deriving the Born and measurement update rules from the other postulates.

Coherence and Asymmetry Cannot be Broadcast

Coherence and asymmetry are valuable resources in quantum metrology and thermodynamics. Here we prove a general no-go theorem: they cannot be reused catalytically on any finite-dimensional system, even if we allow the generation of correlations or entanglement between the systems.

Structure of Reversible Computation Determines the Self-Duality of Quantum Theory

Quantum theory has the remarkable feature of *self-duality*: states and measurement outcomes are described (up to normalization) by the exact same mathematical objects. Here, we prove that this feature is a consequence of *bit symmetry*: any probabilistic theory for which all logical bits are equivalent must be self-dual.

Stationary algorithmic probability

Kolmogorov complexity and algorithmic probability are always defined relative to a choice of universal computer. Can we get rid of this machine-dependence? Here, I give a natural idea for how this might be accomplished, but prove that, in the end, it cannot because of the existence of computer viruses and computable symmetries.

Quantum measurement occurrence is undecidable

We show that a simple problem of quantum information theory is formally undecidable — that is, there does not exist any algorithm that determines the answer in all cases in a finite amount of time. Importantly, the analogous classical problem is (difficult, but) decidable.

Strongly Universal Quantum Turing Machines and Invariance of Kolmogorov Complexity

We prove a key result for the development of a quantum version of Kolmogorov complexity: we show that there are quantum Turing machines that simulate every other QTM, and halt exactly with probability one if the simulated machine does so.

Law without law: from observer states to physics via algorithmic information theory

An approach to the foundations of physics in which not an external world, but a mathematical notion of the first person (“self”) is fundamental. The goal is not philosophical contemplation, but concrete predictions for puzzling thought experiments on physics, agents, computation, and cosmology. More here.

Spin-bounded correlations: rotation boxes within and beyond quantum theory

How can probabilities of events respond to spatial rotations, in any physical theory? We show that quantum theory admits all possible rotational correlations for spins 0, 1/2, and 1, but there are metrological games that can be won with higher probability via beyond-quantum spin-3/2 systems.

Entanglement-Asymmetry Correspondence for Internal Quantum Reference Frames

The Page-Wootters mechanism replaces background time by quantum correlations with a clock. Here we prove that the amount of entanglement with the clock tells us exactly how much time asymmetry is induced in the system, and this holds more generally for arbitrary symmetries and quantum reference frames.

Higher-order interference and single-system postulates characterizing quantum theory

We derive quantum theory from four postulates that only refer to *single* systems, and not to composition: Spectrality, Strong Symmetry, No 3rd-order Interference, and Energy Observability.

Thermalization and Canonical Typicality in Translation-Invariant Quantum Lattice Systems

We give a rigorous proof of *thermalization from entanglement*: for translation-invariant quantum systems, almost all pure global states with large enough energy spread are locally for most times close to a Gibbs state.

Stochastic Independence as a Resource in Small-Scale Thermodynamics

We show that creating correlations between initially uncorrelated systems can enable otherwise impossible state transitions in the resource theory of thermodynamics — the exact opposite of what one might naively expect with standard intuition.

Concentration of Measure for Quantum States with a Fixed Expectation Value

We use integral geometry and techniques by Gromov to prove that almost all pure quantum states with a fixed (say, energy) expectation value behave similarly to the ensemble mean. This has important implications for the quantum thermodynamic behavior of such ensembles.

## Earlier Works

**Fractional sums: how to add a non-integer number of terms**

As a teenager, I developed a theory that extends the definition of sum series to a non-integer number of terms. This works surprisingly well, and leads to beautiful relations to special functions and constants. Learn more

**Debunking an alleged “antigravity” experiment**

In 1997, an American inventor (John Schnurer) claimed to have found a simple way to shield gravity with a superconductor. We reproduced his experiment and found that he seems to have mis-interpreted a simple buoyancy effect. Learn more

**How to iterate functions a non-integer number of times, including “pentation“**

One often studies chaotic behavior by iterating a function a finite number (n=1,2,3, …) of times. As a teenager, I found a natural way to extend this to non-integer n. Learn more