Quantum Foundations

This series is a crash course introduction to a handful of advanced topics designed to tackle the general problem of how to engineer Positive Operator-Valued Measures (POVMs) using observable building blocks, the so-called Instrument Manifold Program.  This program emerged from a recent fundamental breakthrough: how to realize the measurement of a spin’s direction, a.k.a. the spin-coherent-state POVM, a spherical set of outcomes analogous to the well known coherent-state POVM of the standard phase plane.

Outline: Oct 27: Introduction: The Planimeter and the "Spherimeter'' Oct 30: Supplement Nov 03: CANCELLED Nov 06: Supplement Nov 10: POVMs and Decoherence Nov 13: Supplement Nov 17: Generalized Observables: Phase-Point and Spin-Direction Nov 20: Supplement Nov 24: Transformation Groups and Enveloping Algebras Nov 27: Supplement Dec 01: Frame Operators and Quasi-Probability Distributions Dec 04: Supplement Dec 08: The Arthurs-Kelly (1965) and D’Ariano (2002) Measurements Dec 11: Supplement

Location & Building Access: Alice Room, 3rd Floor, Perimeter Institute, 31 Caroline St N, Waterloo (Exception - November 27 in Space Room, 4th Floor)

Registration: Please sign-up here: https://forms.office.com/r/dEA4EUq0CU

Participants who do not have an access card for Perimeter Institute must sign in at the security desk before each session. For information on parking or accessibility please contact [email protected].

In the last few years, a new perspective on probabilistic reasoning has been extensively developed with the help of tools from category theory. The idea is to shift focus from the measure-theoretic details to structural properties of information flow in the presence of uncertainty - independence, conditioning, nested uncertainty, etc. This shift allows one to reason without the need to specify a concrete model of uncertainty, be it discrete, continuous, Gaussian, possibilistic or one of many other instantiations. In this course I will present a high-level overview of the leading approach to categorical probability that is based on so-called Markov categories. We will focus on the diagrammatic language of Markov categories that can be understood without any knowledge of category theory. Using such diagrams, we can also express basic concepts that have been useful in proving a plethora of categorical versions of classical theorems - strong law of large numbers, de Finetti's theorem, d-separation criterion for Bayesian networks, ergodic decomposition theorem, zero/one laws and others.

Location & Building Access: Alice Room, 3rd Floor, Perimeter Institute, 31 Caroline St N, Waterloo

Participants who do not have an access card for Perimeter Institute must sign in at the security desk before each session. For information on parking or accessibility please contact [email protected].

To request the Zoom link for online participation contact [email protected].

Can the effectiveness of a medical treatment be determined without the expense of a randomized controlled trial? Can the impact of a new policy be disentangled from other factors that happen to vary at the same time? Questions such as these are the purview of the field of causal inference, a general-purpose science of cause and effect, applicable in domains ranging from epidemiology to economics. Researchers in this field seek in particular to find techniques for extracting causal conclusions from statistical data. Meanwhile, one of the most significant results in the foundations of quantum theory—Bell’s theorem—can also be understood as an attempt to disentangle correlation and causation. Recently, it has been recognized that Bell’s result is an early foray into the field of causal inference and that the insights derived from almost 60 years of research on his theorem can supplement and improve upon state-of-the-art causal inference techniques. In the other direction, the conceptual framework developed by causal inference researchers provides a fruitful new perspective on what could possibly count as a satisfactory causal explanation of the quantum correlations observed in Bell experiments. Efforts to elaborate upon these connections have led to an exciting flow of techniques and insights across the disciplinary divide. This course will explore what is happening at the intersection of these two fields. Instructor: Robert Spekkens/Bindiya Arora Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

This course will cover the basics of Quantum Foundations under three main headings. Part I – Novel effects in Quantum Theory. A number of interesting quantum effects will be considered. Interferometers: Mach-Zehnder interferometer, Elitzur-Vaidman bomb tester, The quantum-Zeno effect. The no cloning theorem. Quantum optics (single mode). Hong-Ou-Mandel dip. Part II - Conceptual and interpretational issues. Axioms for quantum theory for pure states: Von-Neumann measurement model. * The measurement (or reality) problem. EPR Einstein’s 1927 remarks, the Einstein-Podolsky-Rosen argument. Bell’s theorem, nonlocality without inequalities. The Tirolson bound. The Kochen-Specker theorem and related work by Spekkens On the reality of the wavefunction: Epistemic versus ontic interpretations of the wavefunction and the Pusey-Barrett-Rudolph theorem proving the reality of the wave function. Gleason’s theorem. Interpretations. The landscape of interpretations of quantum theory (the Harrigen Spekkens classification). The de Broglie-Bohm interpretation, the many worlds interpretation, wave- function collapse models, the Copenhagen interpretation, and QBism. Part III - Structural issues. Reformulating quantum theory: we will look at some reformulations of quantum theory and consider the light they throw on the structure of quantum theory. These may include time symmetric quantum theory and weak measurements (Aharonov et al), quantum Bayesian networks, and the operator tensor formalism. Generalised probability theories: These are more general frameworks for probabilistic theories which admit classical and quantum as special cases. Reasonable principles for quantum theory: we will review some of the recent work on reconstructing quantum theory from simple principles. Indefinite causal structure and indefinite causal order. Finally we will conclude by looking at (i) the close link between quantum foundations and quantum information and (ii) possible future directions in quantum gravity motivated by ideas from quantum foundations. Instructor: Lucien Hardy/Bindiya Arora Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

Understanding causality is fundamental to science and inspires wide-ranging applications, yet there are several distinct notions of causation. Recently, there have been important developments on the role of causality in quantum physics, relativistic physics and their interplay. These have unearthed a plethora of fascinating open questions regarding the nature of causation, emergence of space-time structure and the limits of quantum information processing. At the same time, causal reasoning has become an important tool in machine learning and statistics, with applications ranging from big data to healthcare. This conference brings together experts from different areas of physics working on questions related to causality, as well as selected researchers who bridge the gap between fundamental research and current industrial applications. The aim of the conference is to provide a venue for cross-pollination of these ideas through scientific exchange between these communities. The conference will focus on the following facets of causality:

 

• Quantum and classical causal inference

• Indefinite causal order and quantum reference frames

• Causality in quantum field theory and quantum gravity

• Experiments and applications of causality

 

Sponsored in part by:

 

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Prospective speakers can submit a paper for a contributed talk (in person or online) and/or a poster (in person only) via the Call for Abstracts. The Call for Abstracts is now open! Submissions for a talk will automatically be considered for a poster if not accepted for a talk. 

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Invited Speakers

Jessica Bavaresco (University of Geneva)
Cyril Branciard (CNRS, University Grenoble Alpes)
Rafael Chaves (Federal University of Rio Grande do Norte)
Giulio Chiribella (The University of Hong Kong)
Doreen Fraser (University of Waterloo)
Anne-Catherine de la Hamette (IQOQI Vienna)
Ciarán Lee (Spotify)
Tein van der Lugt (University of Oxford)
Joris M. Mooij (University of Amsterdam)
Mio Murao (University of Tokyo)
Alejandro Pozas-Kerstjens (University of Geneva)
Huw Price (Trinity College, Cambridge)
Renato Renner (ETH Zürich)
Thomas Richardson (University of Washington)
Sally Shrapnel (The University of Queensland)
Sumati Surya (Raman Research Institute)
Rainer Verch (University of Leipzig)

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Programme Committee

V Vilasini (ETH Zürich & Inria, University Grenoble Alpes) (PC Chair)
Augustin Vanrietvelde (Télécom Paris) (PC Co-chair)
Alastair Abbott (Inria, University Grenoble Alpes)
Časlav Brukner (IQOQI Vienna & University of Vienna)
Eric Cavalcanti (Griffith University)
Chris Fewster (University of York)
Lucien Hardy (Perimeter Institute)
Hlér Kristjánsson (Perimeter Institute & IQC & Université de Montréal)
Giulia Rubino (University of Bristol)
Nitica Sakharwade (Università degli Studi di Napoli Federico II)
Robert Spekkens (Perimeter Institute)
Jacopo Surace (Perimeter Institute)
Elie Wolfe (Perimeter Institute)
Lin-Qing Chen (ETH Zürich & IQOQI Vienna)
Hippolyte Dourdent (ICFO Barcelona)
Tamal Guha (University of Hong Kong)
Robin Lorenz (Quantinuum, Oxford)
Maria Papageorgiou (IQOQI Vienna)
Nicola Pinzani (Université libre de Bruxelles)
Marco-Túlio Quintino (Sorbonne Université, Paris)
Marc-Olivier Renou (Inria Paris-Saclay & CPHT, École polytechnique)
David Schmid (ICTQT, University of Gdańsk)
John Selby (ICTQT, University of Gdańsk)
Akihito Soeda (National Institute of Informatics, Tokyo)
Matthew Wilson (University College London)
 

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Scientific Organizers

Hlér Kristjánsson (Perimeter Institute & IQC & Université de Montréal) (Chair)
V Vilasini (ETH Zürich & Inria, University Grenoble Alpes) 
Robert Spekkens (Perimeter Institute)
Lucien Hardy (Perimeter Institute)
Elie Wolfe (Perimeter Institute)
Jacopo Surace (Perimeter Institute)
Marina Maciel Ansanelli (Perimeter Institute)
Yìlè Yīng (Perimeter Institute)
María Ciudad Alañón (Perimeter Institute)
Daniel Centeno Díaz (Perimeter Institute)
Khushi Gandhi (Perimeter Institute & University of Waterloo)

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Previous editions:

Causalworlds 2022: The interface between quantum and relativistic causality, foundations and practicalities
Organised at ETH Zürich in 2022. Website: https://causalworlds.ethz.ch/"

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.