April 2025

The no-go theorems of Bell and Kochen and Specker could be interpreted as implying that the notions of system and experimental context are fundamentally inseparable. In this interpretation, statements such as “spin is ‘up’ along direction $x$” are relational statements about the configurations of macroscopic devices which are mediated by the spin and not about any intrinsic properties of the spin. The operational meaning of these statements is provided by the practically infinite resources of macroscopic devices that serve to define the notion of a direction in three-dimensional space. This is the subject of “textbook quantum mechanics”: The description of quantum systems in relation to an experimental context.. Can one go beyond that? Relational quantum mechanics endeavors to provide a relational description between any quantum systems without the necessity of involving macroscopic devices. However, by applying “textbook quantum mechanics” in such situations, it implicitly assumes infinite resources, even for simple quantum systems such as spins, which have no capacity to define an experimental context. This leads to conceptual difficulties. We analyse Penrose’s spin network proposal as a potential formalisation of quantum theory that goes beyond the textbook framework: A description in presence of finite resources, which is inherently relational and inseparable in the system-context entity.

Arguments by Sorkin arXiv:gr-qc/9302018 and Borsten, Jubb, and Kells arXiv:1912.06141 establish that a natural extension of quantum measurement theory from non-relativistic quantum mechanics to relativistic quantum theory leads to the unacceptable consequence that expectation values in one region depend on which unitary operation is performed in a spacelike separated region. Sorkin labels such scenarios “impossible measurements”. We explicitly present these arguments as a no-go result with the logical form of a reductio argument and investigate the consequences for measurement in quantum field theory (QFT). Sorkin-type impossible measurement scenarios clearly illustrate the moral that Microcausality is not by itself sufficient to rule out superluminal signalling in relativistic quantum theories that use Lüders’ rule. We review three different approaches to formulating an account of measurement for QFT and analyze their responses to the “impossible measurements” problem. Two of the approaches are: a measurement theory based on detector models proposed in Polo-Gómez, Garay, and Martín-MartÍnez arXiv:2108.02793 and a measurement framework for algebraic QFT proposed in Fewster and Verch arXiv:1810.06512. Of particular interest for foundations of QFT is that they share common features that may hold general morals about how to represent measurement in QFT. These morals are about the role that dynamics plays in eliminating “impossible measurements”, the abandonment of the operational interpretation of local algebras as representing possible operations carried out in a region, and the interpretation of state update rules. Finally, we examine the form that the “impossible measurements” problem takes in histories-based approaches and we discuss the remaining challenges.

Pointlike systems coupled to quantum fields are often employed as toy models for measurements in quantum field theory. In this paper, we identify the field observables recorded by such models. We show that in models that work in the strong coupling regime, the apparatus is correlated with smeared field amplitudes, while in models that work in weak coupling the apparatus records particle aspects of the field, such as the existence of a particle-like time of arrival and resonant absorption. Then, we develop an improved field-detector interaction model, adapting the formalism of Quantum Brownian motion, that is exactly solvable. This model confirms the association of field and particle properties in the strong and weak coupling regimes, respectively. Further, it can also describe the intermediate regime, in which the field-particle characteristics `merge’. In contrast to standard perturbation techniques, this model also recovers the relativistic Breit-Wigner resonant behavior in the weak coupling regime. The modulation of field-particle-duality by a single tunable parameter is a novel feature that is, in principle, experimentally accessible.

The Newton-Wigner states and operator are widely accepted to provide an adequate notion of spatial localization of a particle in quantum field theory on a spacelike hypersurface. Replacing the spacelike with a timelike hypersurface, we construct one-particle states of massive Klein-Gordon theory that are localized on the hypersurface in the temporal as well as two spatial directions. This addresses the longstanding problem of a “time operator” in quantum theory. It is made possible by recent advances in quantization on timelike hypersurfaces and the introduction of evanescent particles. As a first application of time-localized states, we consider the time-of-arrival problem. Our results are in accordance with semiclassical expectations of causal propagation of massless and massive particles. As in the Newton-Wigner case, localization is not perfect, but apparent superluminal propagation is exponentially suppressed.

Wigner’s friend experiment and its modern extensions display the ambiguity of the quantum mechanical description regarding the assignment of quantum states. While the friend applies the state-update rule to the system upon observing an outcome of her measurement in a quantum system, Wigner describes the friend’s measurement as a unitary evolution, resulting in an entangled state for the composite system of the friend and the system. In this respect, Wigner is often referred to as a “superobserver” who has the supreme technological ability to keep the friend’s laboratory coherent. As such, it is often argued that he has the “correct” description of the state. Here we show that the situation is more symmetrical than is usually thought: there are different types of information that each of the observers has that the other fundamentally cannot have – they reside in different “bubbles” (in Calvalcanti’s terminology). While this can explain why the objectivity of the state assignment is only relative to the bubble, we consider more elaborated situations in form of a game in which the players can switch between bubbles. We find that, in certain circumstances, observers may be entitled to adopt and verify the state assignment from another bubble if they condition their predictions on all information that is in principle available to them.

Motivated by recent advances in non-Lorentzian physics, we revisit the light-cone formulation of quantum field theories. We discuss some interesting subalgebras within the light-cone Poincar’e algebra, with a key emphasis on the Carroll, Bargmann, and Galilean kinds. We show that theories on the light front possess a Hamiltonian of the magnetic Carroll type, thereby proposing a straightforward method for deriving magnetic Carroll Hamiltonian actions from Lorentzian field theories.

Central to near-term quantum machine learning is the use of hybrid quantum-classical algorithms. This paper develops a formal framework for describing these algorithms in terms of string diagrams: a key step towards integrating these hybrid algorithms into existing work using string diagrams for machine learning and differentiable programming. A notable feature of our string diagrams is the use of functor boxes, which correspond to a quantum-classical interfaces. The functor used is a lax monoidal functor embedding the quantum systems into classical, and the lax monoidality imposes restrictions on the string diagrams when extracting classical data from quantum systems via measurement. In this way, our framework provides initial steps toward a denotational semantics for hybrid quantum machine learning algorithms that captures important features of quantum-classical interactions.

These are lectures notes prepared for a series of seminars I am invited to give at Princeton Philosophy Department in November 2024. They cover the conceptual structure of quantum gravity, the relational interpretation of quantum mechanics, the structure of time, its orientation and the openness of the future, the physical underpinning of information and meaning, and some general considerations on the fact that concepts evolve, on perspectivalism and anti-foundationalism.

We introduce a Hamiltonian framework tailored to degrees of freedom (DOF) of field theories that reside in suitable 3-dimensional open regions, and then apply it to the gravitational DOF of general relativity. Specifically, these DOF now refer to open regions of null infinity, and of black hole (and cosmological) horizons representing equilibrium situations. At null infinity the new Hamiltonian framework yields the well-known BMS fluxes and charges. By contrast, all fluxes vanish identically at black hole (and cosmological) horizons just as one would physically expect. In a companion paper we showed that, somewhat surprisingly, the geometry and symmetries of these two physical configurations descend from a common framework. This paper reinforces that theme: Very different physics emerges in the two cases from a common Hamiltonian framework because of the difference in the nature of degrees of freedom. Finally, we compare and contrast this Hamiltonian approach with those available in the literature.

Recent studies have shown that quantum information may be effectively transmitted by a finite collection of completely depolarizing channels in a coherent superposition of different orders, via an operation known as the quantum $tt SWITCH$. Such results are quite remarkable, as completely depolarizing channels taken in isolation and in a definite order can only output white noise. For general channels however, little is known about the potential communication enhancement provided by the quantum $tt SWITCH$. In this Letter, we define an easily computable quantity $mathcal{P}_n$ associated with the quantum ${tt SWITCH}$ of $n$ copies of a fixed channel, and we conjecture that $mathcal{P}_n>0$ is both a necessary and sufficient condition for communication enhancement via the quantum $tt SWITCH$. In support of our conjecture, we derive a simple analytic expression for the classical capacity of the quantum $tt SWITCH$ of $n$ copies of an arbitrary Pauli channel in terms of the quantity $mathcal{P}_n$, which we then use to show that our conjecture indeed holds in the space of all Pauli channels. Utilizing such results, we then formulate a communication protocol involving the quantum $tt SWITCH$ which enhances the private capacity of the BB84 channel.