Quantum Foundations

In classical systems, the Kolmogorov–Arnold–Moser (KAM) theorem establishes that resonant tori of integrable Hamiltonians are destroyed by any nonintegrable perturbation, whereas nonresonant tori are only deformed up to a finite value of the perturbation parameter. In this seminar, we explore a quantum analog of this differentiated sensitivity for one-degree-of-freedom spin Hamiltonians subject to periodic instantaneous kicks. After detecting quantum signatures of resonances in the participation ratio and in the quasiprobability phase-space distribution of Floquet eigenstates of the perturbed Hamiltonian, we show that eigenstates of the unperturbed Hamiltonian exhibit greater sensitivity against the perturbation when they satisfy a resonant condition. The sensitivity is quantified through the fidelity between perturbed and unperturbed eigenstates. This differentiated sensitivity becomes increasingly pronounced as the system size grows. Our findings are supported by numerical results and insights from analytical calculations based on unitary perturbation theory. Although our analysis focuses on kicked models, the mechanism could be extended to more general periodic drivings, providing a preliminary step toward a quantum counterpart of the classical breaking of resonant tori in weakly perturbed integrable systems. Reference: arXiv:2504.13257. 

Measurement is a fundamental ingredient of quantum theory, and reasonably well-understood in non-relativistic quantum mechanics. In contrast, relativistic requirements of locality and causality have provided a challenge for measurement in quantum field theory, as highlighted by Sorkin's seminal work. A second challenge is compositionality: Instead of the simple linear composition in terms of temporal order of the non-relativistic setting, we want to describe joint measurements arbitrarily distributed over different regions of spacetime. A third challenge is that we want to describe the measurement of specific observables and allow for time-extended observables. Progress on the first challenge has been made mostly in an ancilla setting, where an additional system is introduced that models a measurement apparatus. Instead, I focus in this talk on recent results that show how all three challenges can be addressed at a fundamental level.

Although there are good reasons to believe that quantum states are sometimes relativized to observers, there are difficulties for the view that quantum states can only be relativized to conscious macroscopic observers, and also for the view that quantum states can be relativized to any physical system. In this talk, I will argue for an alternative `emergence' approach such that we can indeed write down a description relative to any physical system, but the full formalism of quantum theory emerges only in the limit as the reference system becomes large. If this is true, it poses a challenge for attempts to understand the emergence of the classical regime from the quantum world, since our standard quantum descriptions may presuppose a classical system to which they are relativized. I will describe how this idea might give new insight into Extended Wigner's Friend paradoxes and the measurement problem, and then sketch some ideas for how we might generalize beyond quantum mechanics to characterize descriptions relative to other kinds of reference systems.

Non-local games are a powerful tool to distinguish between correlations possible in classical and quantum worlds. Kalai et al. (STOC’23) proposed a compiler that converts multipartite non-local games into interactive protocols with a single prover, relying on cryptographic tools to remove the assumption of physical separation of the players. While quantum completeness and classical soundness of the construction have been established for all multipartite games, quantum soundness is known only in the special case of bipartite games. In this paper, we prove that the Kalai et al.’s compiler indeed achieves quantum soundness for all multipartite compiled non-local games, by showing that any correlations that can be generated in the asymptotic case correspond to quantum commuting strategies. Our proof uses techniques from the theory of operator algebras, and relies on a characterisation of sequential operationally no-signalling strategies as quantum commuting operator strategies in the multipartite case, thereby generalising several previous results. On the way, we construct universal C*- algebras of sequential PVMs and prove a new chain rule for Radon-Nikodym derivatives of completely positive maps on C*-algebras which may be of independent interest.