This series consists of talks in the area of Foundations of Quantum Theory. Seminar and group meetings will alternate.
One of the most important open problems in physics is to reconcile quantum mechanics with our classical intuition. In this talk we look at quantum foundations through the lens of mathematical foundations and uncover a deep connection between the two fields. We show that Cantorian set theory is based on classical concepts incompatible with quantum experiments. Specifically, we prove that Zermelo-Fraenkel axioms of set theory (and the background classical logic) imply a Bell-type inequality.
We establish a tight relationship between two key quantum theoretical notions: non-locality and complementarity.
I present our work on inferring causality in the classical world and encourage the audience to think about possible generalizations to the quantum world. Statistical dependences between observed quantities X and Y indicate a causal relation, but it is a priori not clear whether X caused Y or Y caused X or there is a common cause of both. It is widely believed that this can only be decided if either one is able to do interventions on the system, or if X and Y are part of a larger set of variables.
In the de Broglie-Bohm pilot-wave theory, an ensemble of fermions is not only described by a spinor, but also by a distribution of position beables. If the distribution of positions is different from the one predicted by the Born rule, the ensemble is said to be in quantum non-equilibrium. Such ensembles, which can lead to an experimental discrimination between the pilot-wave theory and standard quantum mechanics, are thought to quickly relax to quantum equilibrium in most cases.
This talk presents two results on the interplay between causality and quantum information flow. First I will discuss about the task of switching the connections among quantum gates in a network. In ordinary quantum circuits, gates are connected in a fixed causal sequence. However, we can imagine a physical mechanism where the connections among gates are not fixed, but instead are controlled by the quantum state of a control system.
The standard approach to quantum nonlocality (Bell's Theorem) relies on the assumption of the existence of "free will". I will explain how to get rid of this mysterious assumption in favor of the independence of sources. From this new point of view, Bell's Theorem becomes a statement about Bayesian networks. Besides allowing a more intuitive formulation of the standard result, our formalism also provides new network topologies giving rise to new kinds of nonlocality. Some of these relate to results by Steudel and Ay on the statistical inference of causal relations.
We present a quantization method based on theEhrenfest theorem embedded in an extended algebraic structure capableof consistently describing hybrid quantum-classical systems, where thestandard quantum and classical mechanics are two limiting cases. TheWigner phase space formulation and the Schordinger equation are foundto be two alternative representations of the quantum case while theKoopman-von Neumann equation is the corresponding classicalcounterpart.
Categorical quantum mechanics (CQM) uses symmetric monoidal categories to formalize quantum theory, in order to extract the key structures that yield protocols such as teleportation in an abstract way. This formalism admits a purely graphical calculus, but the causal structure of these diagrams, and the formalism in general, is unclear. We begin by considering the signaling abilities of probabilistic devices with inputs and outputs and we show how a non-signaling device can become a perfect signaling device under time-reversal.
I will present a new approach to information theoretic foundations of quantum theory, developed in order to encompass quantum field theory and curved space-times. Its kinematics is based on the geometry of spaces of integrals on W*-algebras, and is independent of probability theory and Hilbert spaces. It allows to recover ordinary quantum mechanical kinematics as well as emergent curved space-times.
©2012 Institut Périmètre de Physique Théorique