Foundations of Quantum Mechanics

Conference Date: 
Monday, July 30, 2018 (All day) to Friday, August 3, 2018 (All day)
Scientific Areas: 
Quantum Foundations
Quantum Information

 

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 30th to August 3rd, 2018.

Registration for this event is now closed.

  • Jonathan Barrett, University of Oxford
  • Bob Coecke, University of Oxford
  • Bianca Dittrich, Perimeter Institute
  • Tobias Fritz, Max Planck Institute for Mathematics in the Sciences
  • Philipp Hoehn, Institute for Quantum Optics and Quantum Information
  • Adrian Kent, University of Cambridge
  • Matthew Leifer, Chapman University
  • Yeong-Cherng Liang, National Cheng Kung University
  • Nuriya Nurgalieva, ETH Zurich
  • Robert Oeckl, Universidad Nacional Autónoma de México
  • Ognyan Oreshkov, Universite Libre de Bruxelles
  • Paolo Perinotti, Universita degli Studi di Pavia
  • Ana Belen Sainz, Perimeter Institute
  • Lev Vaidman, Tel Aviv University
  • Dominic Verdon, University of Oxford
  • Alexander Wilce, Susquehanna University
  • Aida Ahmadzadegan, University of Waterloo & Perimeter Institute
  • Philippe Allard Guerin, University of Vienna
  • Joseph Bramante, Queens University & Perimeter Institute
  • Peter Bruza, Queensland Universityof Technology
  • Justin Dressel, Chapman University
  • Nicholas Gauguin Houghton-Larsen, University of Copenhagen
  • Jose Raul Gonzalez Alonso, Chapman University
  • Sasha Greenfield, Chapman University
  • Aaron Grisez, Chapman University
  • Meenu Kumari, University of Waterloo
  • Marco Letizia, University of Waterloo & Perimeter Institute
  • Robin Lorenz, University of Oxford
  • Robert Mann, University of Waterloo & Perimeter Institute
  • Martin Plavala, Slovak Academy of Sciences
  • Sacha Schwarz, University of Waterloo
  • Andrei Shieber, Perimeter Institute
  • Barak Shoshany, Perimeter Institute
  • Jamie Sikora, Perimeter Institute
  • Michel Vittot, Centre de Physique Theorique
  • Mordecai Waegell, Chapman University
  • Scott Walck, Lebanon Valley College
  • Peter Wittek, University of Toronto
  • Michelle Xu, Perimeter Institute

Monday, July 30, 2018

Time

Event

Location

9:15 – 9:45am

Registration

Reception

9:45 – 10:00am

Lucien Hardy, Perimeter Institute
Welcome and Opening Remarks

Bob Room

10:00 – 11:00am

Jonathan Barrett, University of Oxford
Quantum causal models

Bob Room

11:00 – 11:30pm

Coffee Break

Bistro – 1st Floor

11:30 – 12:30pm

Paolo Perinotti, Universita degli Studi di Pavia
Infinite composite systems and cellular automata in operational probabilistic theories

Bob Room

12:30 – 2:30pm

Lunch

Bistro – 2nd Floor

2:30 – 3:30pm

Robert Oeckl, Universidad Nacional Autónoma de México
Local quantum operations and causality

Bob Room

3:30 – 4:00pm

Coffee Break

Bistro – 1st Floor

4:00 – 5:00 pm

Tobias Fritz, Max Planck Institute for Mathematics in the Sciences
Towards synthetic Euclidean quantum field theory

Bob Room

 

Tuesday, July 31, 2018

Time

Event

Location

10:00 - 11:00am Ana Belen Sainz, Perimeter Institute
Almost quantum correlations violate the no-restriction hypothesis
Bob room

11:00 – 11:10am

Conference Photo

TBA

11:10 – 11:30pm

Coffee Break

Bistro – 1st Floor

11:30 – 12:30pm

Yeong-Cherng Liang, National Cheng Kung University
A device-independent approach to testing
physical theories from finite data

Bob Room

12:30 – 2:30pm

Lunch

Bistro – 2nd Floor

2:30 – 3:30pm

Alexander Wilce, Susquehanna University
Quantum axiomatics à la carte

Bob Room

3:30 – 4:00pm

Coffee Break

Bistro – 1st Floor

4:00 – 5:00pm

Discussion 1

Bob Room

 

Wednesday, August 1, 2018

Time

Event

Location

10:00 – 11:00am

Philipp Hoehn, Institute for Quantum Optics & Quantum Information
Quantum reference systems: Where foundations meets gravity

Bob Room

11:00 – 11:30pm

Coffee Break

Bistro – 1st Floor

11:30 - 12:30pm Bianca Dittrich, Perimeter Institute
Observables and (no) time in quantum gravity
Bob Room

12:30 – 2:30pm

Lunch

Bistro – 2nd Floor

2:30 – 3:30pm

Matthew Leifer, Chapman University
Measures of Preparation Contextuality

Bob Room

3:30 – 4:00pm

Coffee Break

Bistro – 1st Floor

4:00 – 5:00pm

Discussion 2

Bob Room

 

Thursday, August 2, 2018

Time

Event

Location

10:00 – 11:00am

Dominic Verdon, University of Oxford
A compositional approach to quantum functions, and the Morita theory of quantum graph isomorphisms

Bob Room

11:00 – 11:30pm

Coffee Break

Bistro – 1st Floor

11:30 – 12:30pm

Bob Coecke, University of Oxford
From quantum to cognition in pictures.

Bob Room

12:30 – 2:30pm

Lunch

Bistro – 2nd Floor

2:30 – 3:30pm

Adrian Kent, University of Cambridge
Models and Tests of Quantum Theory and Gravity

Bob Room

3:30 – 4:00pm

Coffee Break

Bistro – 1st Floor

4:00 – 5:00pm

Discussion 3

Bob Room

6:00pm onwards

Banquet

Bistro – 2nd Floor

 

Friday, August 3, 2018

Time

Event

Location

10:00 – 11:00am

Ognyan Oreshkov, Universite Libre de Bruxelles
Time-delocalized quantum subsystems and operations:
on the existence of processes with indefinite causal structure in quantum mechanics

Bob Room

11:00 – 11:30pm

Coffee Break

Bistro – 1st Floor

11:30 – 12:30pm

Lev Vaidman, Tel Aviv University
Counterfactual communication protocols

Bob Room

12:30 – 2:30pm

Lunch

Bistro – 2nd Floor

2:30 – 3:30pm

Nuriya Nurgaliva, ETH Zurich
Observers as Primitives

Bob Room

 

 

Jonathan Barrett, University of Oxford

Quantum causal models

From a brief discussion of how to generalise Reichenbach’s Principle of the Common Cause to the case of quantum systems, I will develop a formalism to describe any set of quantum systems that have specified causal relationships between them. This formalism is the nearest quantum analogue to the classical causal models of Judea Pearl and others. At the heart of the classical formalism lies the idea that facts about causal structure enforce constraints on probability distributions in the form of conditional independences. I will describe a quantum analogue of this idea, which leads to a quantum version of the three rules of Pearl’s do-calculus. If time, I will end with some more speculative remarks concerning the significance of the work for the foundations of quantum theory.

Bob Coecke, University of Oxford

From quantum to cognition in pictures.

For well over a decade, we developed an entirely pictorial (and formally rigorous!) presentation of quantum theory [*].  At the present, experiments are being setup aimed at establishing the age at which children could effectively learn quantum theory in this manner.  Meanwhile, the pictorial language has also been successful in the study of natural language, and very recently we have started to apply it to model cognition, where we employ GPT-alike models.  We present the key ingredients of the pictorial language language as well as their interpretation across disciplines.
 
[*] B. Coecke & A. Kissinger (2017) Picturing Quantum Processes. A first course on quantum theory and diagrammatic reasoning.  Cambridge University Press.
 
Bianca Dittrich, Perimeter Institute
 
Observables and (no) time in quantum gravity
 
I will explain the special requirements that observables have to satisfy in quantum gravity and how this affects deeply the notion of time. I will furthermore explore how the search for observables in classical gravity can inform the construction of a quantum theory of gravity.
 
Tobias Fritz, Max Planck Institute for Mathematics in the Sciences
 
Towards synthetic Euclidean quantum field theory
 
In this status report on current work in progress, I will sketch a generalization of the <a href="https://arxiv.org/abs/1710.10258">temporal type theory</a> introduced by Schultz and Spivak to a logic of space and spacetime. If one writes down a definition of probability space within this logic, one conjecturally obtains a notion whose semantics is precisely that of a Euclidean quantum field. I will sketch how to use the logic to reason about probabilities of events involving fields, sketch the relation to AQFT, and attempt to formulate the DLR equations within the logic.
 
Joint work with David Spivak
 
Philipp Hoehn, Institute for Quantum Optics and Quantum Information
 
Quantum reference systems: Where foundations meets gravity
 
Quantum foundations and (quantum) gravity are usually considered independently. However, I will demonstrate by means of quantum reference systems how tools and perspectives from quantum gravity can help to solve problems in quantum foundations and, conversely, how quantum foundation perspectives can be useful to constrain spacetime structures.
 
First, I will show how one can derive transformations between quantum reference frames from a gravity inspired symmetry (essentially Mach’s) principle. This principle enforces a perspective neutral theory in which choosing the perspective of a specific frame becomes a choice of gauge and all physical information is relational. This setting enables one to derive and generalize, from first principles, frame transformations that have been proposed earlier in the foundations literature. Moreover, the framework extends to the relational paradigm of dynamics, familiar from quantum gravity, and thereby provides a unifying method for changes of perspective in the quantum theory, incl. changes of both spatial and temporal quantum reference systems.
 
Subsequently, I will take a quantum information inspired perspective on frame synchronization and transformations. Without presupposing specific spacetime structure, I will exhibit how the Lorentz group follows from operational conditions on quantum communication, exemplifying how quantum information protocols can constrain the spacetime structures in which they are feasible.
 
Adrian Kent, University of Cambridge
 
Models and Tests of Quantum Theory and Gravity
 
Models that have some but not all features of standard quantum theory can be valuable in several ways, as Bell, Ghirardi-Rimini-Weber-Pearle, Hardy, Spekkens and many others have shown.  One is to illuminate quantum theory and shed light on  possible reaxiomatisations or reformulations.   Another is to suggest experiments that might confirm some untested aspect of quantum theory or point the way to a new theory.    I discuss here some models that combine quantum theory and gravity and experimental tests. 
 
Matthew Leifer, Chapman University
 
Measures of Preparation Contextuality
 
In a large medical trial, if one obtained a ridiculously small p-value like 10^-12, one would typically move from a plain hypothesis test to trying to estimate the parameters of the effect.  For example, one might try to estimate the optimal dosage of a drug or the optimal length of a course of treatment.  Tests of Bell and noncontextuality inequalities are hypotheses tests, and typical p-values are much lower than this, e.g. 12-sigma effects are not unheard of and a 7-sigma violation already corresponds to a p-value of about 10^-12.  Why then, in quantum foundations, are we still obsessed with proposing and testing new inequalities rather than trying to estimate the parameters of the effect from the experimental data?  Here, we will try to do this for preparation contextuality, but will also make some related comments on recent loophole-free Bell inequality tests.
 
We introduce two measures of preparation contextuality: the maximal overlap and the preparation contextuality fraction.  The latter is linearly related to the degree of violation of a preparation noncontextuality inequality, so can be estimated from experimental data. Although the measures are different in general, they can be equal for proofs of preparation contextuality that have sufficient symmetry, such as the timelike analogue of the CHSH scenario.  We give the value of these measures for this scenario.  Using our result, we can consider pairty-epsilon multiplexing, Alice must try to communicate two bits to Bob so that he can choose to determine either of them with high probability, but where Alice must ensure that Bob cannot guess the parity of the bits with probability greater than 1/2 + epsilon, and determine the range of epislon for which there is still an advantage in preparation contextual theories.  If time permits, I will make some brief comments on how to robustify experimental tests of this result.
 
joint work with Eric Freda and David Schmid
 
Yeong-Cherng Liang, National Cheng Kung University
 
A device-independent approach to testing physical theories from finite data
 
The device-independent approach to physics is one where conclusions are drawn directly and solely from the observed correlations between measurement outcomes. This operational approach to physics arose as a byproduct of Bell's seminal work to distinguish quantum correlations from the set of correlations allowed by locally-causal theories. In practice, since one can only perform a finite number of experimental trials, deciding whether an empirical observation is compatible with some class of physical theories will have to be carried out via the task of hypothesis testing. In this talk, I will review some recent progress on this task based on the prediction-based-ratio method and discuss how it may allow us to falsify, in principle, other classes of physical theories, such as those constrained only by the nonsignaling principle, and those that are constrained to produce the so-called "almost-quantum" set of correlations. As an application, I demonstrate how this method allows us to unveil the apparent violation of the nonsignaling conditions in certain experimental data collected in a Bell test. The lesson learned from this observation will be briefly discussed.
 
Nuriya Nurgalieva, ETH Zurich
 
Observers as Primitives
 
Let us suppose that we are trying to build a physical theory of the universe, in order to do so, we have to introduce some primitive notions, on which the theory will be based upon.  We explore possible candidates that can be considered to be such "primitives": for example, the structure of the spacetime, or quantum states.  However, the examples can be given such that show that these notions are not as objective as we would want them to be.  The concept of objectivity, on the other hand, is closedly linked to that one of "an observer", thus, we can at least assign it as a primitive of the theory.  Now agents are themselves physical systems, and we should take this into account when we specify the ground rules of what they can do.  On the one hand, we take agents and their communication as a primitive of the theory and then see which concepts can be derived from there.  On the other hand, we treat agents as quantum systems themselves and investigate what kind of logic applies to their interpersonal reasoning; for that, as a guiding example we use the Frauchiger-Renner thought experiment {1,2}.
 
Robert Oeckl, Universidad Nacional Autónoma de México
 
Local quantum operations and causality
 
I give further details on a unification of the foundations of operational quantum theory with those of quantum field theory, coming out of a program that is also known as the positive formalism. I will discuss status and challenges of this program, focusing on the central new concept of local quantum operation. Among the conceptual challenges I want to highlight the question of causality. How do we know that future choices of measurement settings do not influence present measurement results? Should we enforce this, as in the standard formulation of quantum theory? Should this "emerge" from a fundamental theory? Does this question even make sense in a context without a fixed notion of time, such as quantum gravity? With a heavy dose of speculation (put also grounded in very concrete evidence) I find that fermionic theories might play an essential role.
 
Ognyan Oreshkov, Universite Libre de Bruxelles
 
Time-delocalized quantum subsystems and operations: on the existence of processes with indefinite causal structure in quantum mechanics
 
It was recently found that it is theoretically possible for there to exist higher-order quantum processes in which the operations performed by separate parties cannot be ascribed a definite causal order. Some of these processes are believed to have a physical realization in standard quantum mechanics via coherent control of the times of the operations. A prominent example is the quantum SWITCH, which was recently demonstrated experimentally. However, up until now, there has been no rigorous justification for the interpretation of such an experiment as a genuine realization of a process with indefinite causal structure as opposed to a simulation of such a process. Where exactly are the local operations of the parties in such an experiment? On what spaces do they act given that their times are indefinite? Can we probe them directly rather than assume what they ought to be based on heuristic considerations? How can we reconcile the claim that these operations really take place, each once as required, with the fact that the structure of the presumed process implies that they cannot be part of any acyclic circuit? Here, I offer a precise answer to these questions: the input and output systems of the operations in such a process are generally nontrivial subsystems of Hilbert spaces that are tensor products of Hilbert spaces associated with different times—a fact that is directly experimentally verifiable. With respect to these time-delocalized subsystems, the structure of the process is one of a circuit with a cycle, which cannot be reduced to a (possibly dynamical) probabilistic mixture of acyclic circuits. This provides, for the first time, a rigorous proof of the existence of processes with indefinite causal structure in quantum mechanics. I further show that all bipartite processes that obey a recently proposed unitary extension postulate, together with their unitary extensions, have a physical realization on such time-delocalized subsystems, and provide evidence that even more general processes may be physically admissible. These results unveil a novel structure within quantum mechanics, which may have important implications for physics and information processing.
 
Paolo Perinotti, Universita degli Studi di Pavia
 
Infinite composite systems and cellular automata in operational probabilistic theories
 
Cellular automata are a central notion for the formulation of physical laws in an abstract information-theoretical scenario, and lead in recent years to the reconstruction of free relativistic quantum field theory. In this talk we extend the notion of a Quantum Cellular Automaton to general Operational Probabilistic Theories. For this purpose, we construct infinite composite systems, illustrating the main features of their states, effects and transformations. We discuss the generalization of the concepts of homogeneity and locality, in an framework where space-time is not a primitive object. We show that homogeneity leads to a Cayley graph structure of the memory array, thus proving the universality of the connection between homogeneity and discrete groups. We conclude illustrating the special case of Fermionic cellular automata, discussing three relevant examples: Weyl and Dirac quantum walks, the Thirring automaton and the simplest families of automata on finite graphs.
 
Ana Belen Sainz, Perimeter Institute
 
Almost quantum correlations violate the no-restriction hypothesis
 
To identify which principles characterise quantum correlations, it is essential to understand in which sense this set of correlations differs from that of almost quantum correlations. We solve this problem by invoking the so-called no-restriction hypothesis, an explicit and natural axiom in many reconstructions of quantum theory stating that the set of possible measurements is the dual of the set of states. We prove that, contrary to quantum correlations, no generalised probabilistic theory satisfying the no-restriction hypothesis is able to reproduce the set of almost quantum correlations. Therefore, any theory whose correlations are exactly, or very close to, the almost quantum correlations necessarily requires a rule limiting the possible measurements. Our results suggest that the no-restriction hypothesis may play a fundamental role in singling out the set of quantum correlations among other non-signalling ones.
 
Lev Vaidman, Tel Aviv University
 
Counterfactual communication protocols
 
Possibility to communicate between spatially separated regions, without even a single photon passing between the two parties, is an amazing quantum phenomenon. The possibility of transmitting one value of a bit in such a way, the interaction-free measurement, was known for quarter of a century. The protocols of full communication, including transmitting unknown quantum states were proposed only few years ago, but it was shown that in all these protocols the particle was leaving a weak trace in the transmission channel, the trace larger than the trace left by a single particle passing through the channel.  However, a simple modification of these recent protocols eliminates the trace in the transmission channel and makes all these protocols truly counterfactual.
 
Dominic Verdon, University of Oxford
 
A compositional approach to quantum functions, and the Morita theory of quantum graph isomorphisms
 
Certain nonlocal games exhibiting quantum advantage, such as the quantum graph homomorphism and isomorphism games, have composable quantum strategies which are naturally interpreted as structure-preserving functions between finite sets.  We propose a natural compositional framework for noncommutative finite set theory in which these quantum strategies appear naturally, and which connects nonlocal games with recent work on compact quantum groups. We apply Morita-theoretical machinery within this framework to characterise, classify, and construct quantum strategies for the graph isomorphism game. This is joint work with Benjamin Musto and David Reutter, based on the papers 1711.07945 and 1801.09705.
 
Alexander Wilce, Susquehanna University
 
Quantum axiomatics à la carte
 
The past decade or so has produced a handful of derivations, or reconstructions, of finite-dimensional quantum mechanics from various packages of operational and/or information-theoretic principles. I will present a selection of these  principles --- including symmetry postulates, dilational assumptions, and versions of Hardy's subspace axiom --- in a common framework, and indicate several ways, some familiar and some new, in which these can be combined to yield  either standard complex QM (with or without SSRs) or broader theories embracing formally real Jordan algebras.
 
 

 

Friday Aug 03, 2018
Speaker(s): 

Let us suppose that we are trying to build a physical theory of the universe, in order to do so, we have to introduce some primitive notions, on which the theory will be based upon. We explore possible candidates that can be considered to be such "primitives": for example, the structure of the spacetime, or quantum states. However, the examples can be given such that show that these notions are not as objective as we would want them to be.

Scientific Areas: 
 

 

Friday Aug 03, 2018
Speaker(s): 

Possibility to communicate between spatially separated regions, without even a single photon passing between the two parties, is an amazing quantum phenomenon. The possibility of transmitting one value of a bit in such a way, the interaction-free measurement, was known for quarter of a century.

Scientific Areas: 
 

 

Friday Aug 03, 2018
Speaker(s): 

It was recently found that it is theoretically possible for there to exist higher-order quantum processes in which the operations performed by separate parties cannot be ascribed a definite causal order. Some of these processes are believed to have a physical realization in standard quantum mechanics via coherent control of the times of the operations. A prominent example is the quantum SWITCH, which was recently demonstrated experimentally.

Scientific Areas: 
 

 

Thursday Aug 02, 2018
Speaker(s): 

Models that have some but not all features of standard quantum theory can be valuable in several ways, as Bell, Ghirardi-Rimini-Weber-Pearle, Hardy, Spekkens and many others have shown. One is to illuminate quantum theory and shed light on possible reaxiomatisations or reformulations. Another is to suggest experiments that might confirm some untested aspect of quantum theory or point the way to a new theory. I discuss here some models that combine quantum theory and gravity and experimental tests.

Scientific Areas: 
 

 

Thursday Aug 02, 2018
Speaker(s): 

For well over a decade, we developed an entirely pictorial (and formally rigorous!) presentation of quantum theory [*]. At the present, experiments are being setup aimed at establishing the age at which children could effectively learn quantum theory in this manner. Meanwhile, the pictorial language has also been successful in the study of natural language, and very recently we have started to apply it to model cognition, where we employ GPT-alike models. We present the key ingredients of the pictorial language language as well as their interpretation across disciplines.

Scientific Areas: 
 

 

Thursday Aug 02, 2018
Speaker(s): 

Certain nonlocal games exhibiting quantum advantage, such as the quantum graph homomorphism and isomorphism games, have composable quantum strategies which are naturally interpreted as structure-preserving functions between finite sets. We propose a natural compositional framework for noncommutative finite set theory in which these quantum strategies appear naturally, and which connects nonlocal games with recent work on compact quantum groups.

Scientific Areas: 
 

 

Wednesday Aug 01, 2018
Speaker(s): 

In a large medical trial, if one obtained a ridiculously small p-value like 10^-12, one would typically move from a plain hypothesis test to trying to estimate the parameters of the effect. For example, one might try to estimate the optimal dosage of a drug or the optimal length of a course of treatment. Tests of Bell and noncontextuality inequalities are hypotheses tests, and typical p-values are much lower than this, e.g. 12-sigma effects are not unheard of and a 7-sigma violation already corresponds to a p-value of about 10^-12.

Scientific Areas: 
 

 

Wednesday Aug 01, 2018
Speaker(s): 

I will explain the special requirements that observables have to satisfy in quantum gravity and how this affects deeply the notion of time. I will furthermore explore how the search for observables in classical gravity can inform the construction of a quantum theory of gravity.

Scientific Areas: 
 

 

Wednesday Aug 01, 2018
Speaker(s): 

Quantum foundations and (quantum) gravity are usually considered independently. However, I will demonstrate by means of quantum reference systems how tools and perspectives from quantum gravity can help to solve problems in quantum foundations and, conversely, how quantum foundation perspectives can be useful to constrain spacetime structures.

Scientific Areas: 
 

 

Tuesday Jul 31, 2018
Scientific Areas: 

Pages

Scientific Organizers:

  • Lucien Hardy, Perimeter Institute
  • Markus Mueller, Perimeter Institute & Institute for Quantum Optics and Quantum Information, Vienna
  • Prakash Panangaden, McGill University
  • Robert Spekkens, Perimeter Institute

Scientific Organizing Committee:

  • Lucien Hardy, Perimeter Institute
  • Ravi Kunjwal, Perimeter Institute
  • Denis Rosset, Perimeter Institute
  • Nitica Sakharwade, Perimeter Institute
  • John Selby, Perimeter Institute
  • Robert Spekkens, Perimeter Institute
  • Elie Wolfe, Perimeter Institute