Quantum Foundations

The aim of the first part is to present a brief overview of selected topics in quantum theory. Schrodinger, Heisenberg and Interaction picture is discussed and applied to study time evolution. Density matrix and Feynman path integral are introduced. The second part of the course derives the Feynman rules for scalar quantum field theory and introduces renormalization. Instructor: Bindiya Arora / Dan Wohns Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

Classical probability theory makes the (mostly, tacit) assumption that any two random experiments can be performed jointly.  This assumption seems to fail in quantum theory.  A rapidly growing literature seeks to understand QM by placing it in a much broader mathematical landscape of ``generalized probabilistic theories", or GPTs,  in which incompatible experiments are permitted.   Among other things, this effort has led to  (i) a better appreciation that many "characteristically quantum" phenomena (e.g., entanglement)  are in fact generic to non-classical probabilistic theories, (ii) a suite of reconstructions of (mostly, finite-dimensional) QM from small packages of assumptions of a probabilistic or operational nature, and (iii) a clearer view of the options available for generalizing QM.  This course will offer a survey of this literature,  starting from scratch and concluding with a discussion of recent developments. 

Mathematical prerequisites: finite-dimensional linear algebra, ideally including tensor products and duality, plus some exposure to category theory (though I will briefly review this material as needed).  

Scheduling note: There will be 5 lectures from March 12-26, then a gap of two weeks before the final 2 lectures held April 16 & 18.

Format: In-person only; lectures will be recorded for PIRSA but not live on Zoom.

Recently we have seen exciting results at the intersection of quantum foundations and the statistical analysis of causal hypotheses by virtue of the centrality of latent variable models to both fields.

In this workshop we will explore how academics from both sides can move the shared frontiers forward. Towards that end, we are including extensive breakout collaboration opportunities in addition to formal presentations. In order to make concrete progress on problems pertinent to both communities, we have selected the topic of causal models with restricted cardinality of the latent variables as a special focus for this workshop. 

Sponsorship for this workshop has been provided by:

https://pirsa.org/C23017

Territorial Land Acknowledgement

Perimeter Institute acknowledges that it is situated on the traditional territory of the Anishinaabe, Haudenosaunee, and Neutral peoples.

Perimeter Institute is located on the Haldimand Tract. After the American Revolution, the tract was granted by the British to the Six Nations of the Grand River and the Mississaugas of the Credit First Nation as compensation for their role in the war and for the loss of their traditional lands in upstate New York. Of the 950,000 acres granted to the Haudenosaunee, less than 5 percent remains Six Nations land. Only 6,100 acres remain Mississaugas of the Credit land. 

We thank the Anishinaabe, Haudenosaunee, and Neutral peoples for hosting us on their land.

There has been a surge of interest in indefinite causal structure the idea that cause and effect can no longer be sharply distinguished.  Motivated both by experimentation with quantum switches and quantum gravity there can be situations in which there is no matter-of-the-fact as to what the causal structure of spacetime is.  This meeting will bring together workers in Quantum Foundations and Quantum Gravity in both theoretical experimental physics to discuss the state of the art of current research and set new directions for this emerging subdiscipline.

The foundations of quantum mechanics have been revitalized in the past few decades by three developments:  (i) the influence of quantum computation and quantum information theory (ii) studies of the interplay between quantum theory and relativity particularly the analysis of indefinite causal structure and (iii) proposals to reconstruct quantum theory from basic axioms.  There have also been very interesting developments in understanding and classifying no=locality and contextuality using tools from sheaf theory and cohomology as well as operator algebras and category theory. The International Congress of Mathematical Physics is a natural forum for the discussion of these topics.  In the past there have been satellite workshops on topics like Operator algebras and quantum statistical mechanics which also address fundamental issues.  The modern study of quantum foundations is very much influenced and informed by mathematics:  sheaf theory and cohomology category theory information theory convex analysis in addition to the continuing interest in operator algebras and functional analysis. The aim of the workshop is to bring together researchers who have made substantial contribution to the recent developments.  The workshop will be held at Perimeter Institute over a five day period from July 30

Our universe is of astonishing simplicity: almost all physical observations can in principle be described by a few theories that have short mathematical descriptions. But there is a field of computer science which quantifies simplicity namely algorithmic information theory (AIT). In this workshop we will discuss emerging connections between AIT and physics some of which have recently shown up in fields like quantum information theory and thermodynamics. In particular AIT and physics share one goal: namely to predict future observations given previous data. In fact there exists a gold standard of prediction in AIT called Solomonoff induction which is also applied in artificial intelligence. This motivates us to look at a broader question: what is the role of induction in physics? For example can quantum states be understood as Bayesian states of belief? Can physics be understood as a computation in some sense? What is the role of the observer i.e. the agent that is supposed to perform the predictions? These and related topics will be discussed by a diverse group of researchers from different disciplines.

Foil theories sometimes called mathematically rigorous science fiction describe ways the world could have been were it not quantum mechanical. Our understanding of quantum theory has been deepened by contrasting it with these alternatives. So far observers in foil theories have only been modeled implicitly for example via the recorded probabilities of observing events. Even when multi-agent settings are considered these agents tend to be compatible in the classical sense that they could always compare their observations. Scenarios where agents and their memories are themselves modeled as physical systems within the theory (and could in particular measure each other as in Wigner's friend experiment) have not yet been considered. In this workshop we will investigate which foil theories allow for the existence of explicit observers and whether they allow for paradoxes in multi-agent settings such as those found in quantum theory. We will also investigate which interpretations of quantum theory would equally well interpret the foil theories and which interpretations are truly quantum. We will gain a deeper understanding of how this can happen by discussing appropriate definitions observers in these theories and seeing how such observers learn about their environment.