Quantum reference systems: Where foundations meets gravity
Philipp Hoehn Okinawa Institute of Science and Technology Graduate University
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A device-independent approach to testing physical theories from finite data
Yeong-Cherng Liang National Cheng Kung University
Almost quantum correlations violate the no-restriction hypothesis
Ana Belen Sainz Gdańsk University of Technology
Towards synthetic Euclidean quantum field theory
Tobias Fritz Universität Innsbruck
Local quantum operations and causality
Robert Oeckl Universidad Nacional Autónoma De Mexico (UNAM)
Welcome and Opening Remarks
Lucien Hardy Perimeter Institute for Theoretical Physics
Certified Randomness from Quantum Supremacy
Scott Aaronson The University of Texas at Austin
Cosmos, the beginnings...
Ghazal Geshnizjani Perimeter Institute for Theoretical Physics
PIRSA:18070060
Quantum reference systems: Where foundations meets gravity
Philipp Hoehn Okinawa Institute of Science and Technology Graduate University
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.Quantum axiomatics à la carte
Alexander Wilce Susquehanna University
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.A device-independent approach to testing physical theories from finite data
Yeong-Cherng Liang National Cheng Kung University
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.Almost quantum correlations violate the no-restriction hypothesis
Ana Belen Sainz Gdańsk University of Technology
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.Towards synthetic Euclidean quantum field theory
Tobias Fritz Universität Innsbruck
In this status report on current work in progress, I will sketch a generalization of the temporal type theory 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 SpivakLocal quantum operations and causality
Robert Oeckl Universidad Nacional Autónoma De Mexico (UNAM)
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.Infinite composite systems and cellular automata in operational probabilistic theories
Paolo Perinotti University of Pavia
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.
Quantum causal models
Jonathan Barrett University of Oxford
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.Welcome and Opening Remarks
Lucien Hardy Perimeter Institute for Theoretical Physics
Certified Randomness from Quantum Supremacy
Scott Aaronson The University of Texas at Austin
I’ll describe a novel application for near-term quantum computers with 50-70 qubits: namely, generating cryptographic random bits, whose randomness can be certified even if the quantum computer is untrusted (e.g., has been backdoored by an adversary). Unlike schemes based on Bell inequality violation, ours requires only a single device able to solve classically hard sampling problems. Our protocol harvests the outputs of the sampling process and feeds them into a randomness extractor, while occasionally verifying the outputs using exponential classical time. I’ll also compare to the beautiful independent work of Brakerski et al., who proposed a scheme for the same problem that has much more efficient verification, but that probably can’t be implemented on near-term devices. Paper still in preparation.
Cosmos, the beginnings...
Ghazal Geshnizjani Perimeter Institute for Theoretical Physics
PIRSA:18070060Abstract: “How did our universe begin?” is possibly one of the oldest questions that have bewildered humans throughout history. As a theoretical cosmologist, our job is to find a mathematically consistent picture for early universe that could explain observations, from the largest to the smallest scales. The past thirty years have witnessed amazing progress, both in developing technology for precision cosmological observations, and in perfecting mathematical methodology to explain them. For example, ripples in cosmic geometry are now measured with the precision of one part in a million. We also have sophisticated mathematical frameworks such as general relativity and quantum theories that describe the origin of these ripples in early universe. However, with all of these extraordinary achievements, some old and new puzzles remain unsolved. For example we still have not resolved the most crucial puzzle about the origin of cosmos, namely the Big Bang Singularity problem. We will take a journey back in time to explore the fascinating realm of early universe and some of its mysteries.CPT symmetric universe
Latham Boyle University of Edinburgh
PIRSA:18070059Abstract: From astronomical observations, we know that the state of the early universe (just after the Big Bang) was extremely simple. This is surely an important clue about how the universe began, but what exactly is it trying to tell us? I will explain our new answer to this question: we think it is telling us that the universe before the bang is a kind of mirror image of the universe after the bang (they are related by "CPT symmetry"). (Based on recent work with Kieran Finn and Neil Turok: https://arxiv.org/pdf/1803.08928.pdf)