Quantum Foundations

The methodology employed in reconstructing quantum theory involves defining a general mathematical framework that frames a landscape of possible theories and then positing principles that uniquely pick out quantum theory. In contrast, many traditional interpretations of quantum theory consider only quantum theory, not a larger space of possible theories. I will defend the modal methodology used in reconstruction by tracing the historical roots of Einstein’s distinction between principle and constructive theories. Einstein’s principle theories (exemplified by thermodynamics and special relativity) are often cited as inspiration for reconstructing quantum theory. The concept of a “physics of principles” emerged at the end of the nineteenth century in the context of the application of Lagrangian mechanics to electromagnetism. This case is an intriguing historical precedent for reconstructing quantum theory. I will also offer some reflections on how the application of a similar modal methodology in axiomatic QFT plays out. 

Hidden-variables theories account for quantum mechanics in terms of a particular 'equilibrium' distribution of underlying parameters corresponding to the Born rule. In the most well-studied example, the pilot-wave theory of de Broglie and Bohm, it is well established that the Born rule may be understood to arise from a process of dynamical relaxation. This 'quantum relaxation' may have taken place in the very early universe and could have left imprints on the cosmic microwave background (CMB). Such imprints amount to signatures of the decay of early violations of the Born rule. In this colloquium we summarise recent progress in making detailed predictions and in comparing them with the reported large-scale anomalies in the CMB data.

Hidden-variables theories account for quantum mechanics in terms of a particular 'equilibrium' distribution of underlying parameters corresponding to the Born rule. A natural question to ask is whether the theory is stable under small perturbations away from equilibrium. We compare and contrast two examples: de Broglie's 1927 pilot-wave theory and Bohm's 1952 reformulation thereof. It is well established that in de Broglie's dynamics initial deviations from equilibrium will relax. We show that this is not the case for Bohm's dynamics: initial deviations from equilibrium do not relax and in fact grow with time. On this basis we argue that Bohm's dynamics is untenable as a physical theory (while de Broglie's dynamics remains a viable candidate). We advocate stability as a general selection criterion for hidden-variables theories.

In this talk I show how to systematically classify all possible alternatives to the measurement postulates of quantum theory. All alternative measurement postulates are in correspondence with a representation of the unitary group. I will discuss composite systems in these alternative theories and show that they violate two operational properties: purification and local tomography. This shows that one can derive the measurement postulates of quantum theory from either of these properties. I will discuss the relevance of this result to the field of general probabilistic theories. In a second part of the talk I will discuss work in progress and directions for future research. I will show how to generalise the framework used to theories which have different pure states and dynamics than quantum theory. I will discuss two types of theories which can be studied in this framework: Grassmannian theories (same dynamical group and different pure states to quantum theory) and non-linear modifications to the Schrodinger equation (same pure states and different dynamical group).

Science is like puzzle-solving. Making sense of quantum theory is a particularly thorny kind of brain-twister, with more than its fair share of mysteries. If you are stuck on a puzzle, it may be because you have made a false assumption about the nature of some entity that is absolutely central to the whole business. If so, you have made a category mistake: you are not just wrong about what this entity is, but about what sort of thing it is.

In his Public Lecture at Perimeter Institute, Robert Spekkens will explain why he believes that many quantum mysteries are a result of a category mistake concerning the nature of quantum states. Along the way, he will address some idiosyncratic questions, such as: What did Plato have to say about Heisenberg’s uncertainty principle? What do poorly implemented clinical drug trials have to do with "spooky action at a distance"? And, most importantly, what did the successful deciphering of Egyptian hieroglyphs teach us about the interpretation of quantum theory? 

Spekkens is a faculty member at Perimeter Institute whose research examines the foundations of quantum theory. He co-edited the book Quantum Theory: Informational Foundations and Foils, and he is a Project Leader of the international research collaboration "Quantum Causal Structures.” In 2012, he won first prize in the Foundational Questions Institute (FQXi) essay contest "Questioning the Foundations: Which of Our Assumptions Are Wrong?" He lives in Waterloo with his wife and three-year-old son.

In this talk I will discuss recently-identified classes of quantum correlations that go beyond nonlocal classical hidden-variable models equipped with communication. First, in the bipartite scenario, I will focus on so-called instrumental causal networks, which are a primal tool in causal inference. There, I will show that it is possible to “fake” classical causal influences with quantum common causes, in a formal sense quantified by the average causal effect (ACE). Furthermore, I will show that it is possible to violate instrumental inequalities with quantum resources, both in the device-independent and in the 1-sided device-independent settings. Second, in the multipartite setting, I will present a causal hierarchy of multipartite nonlocality. I will make special emphasis on quantum correlations in the upper classes of the hierarchy that define stronger forms of genuinely multipartite quantum non-locality than those previously known. The seminar will touch upon concepts like Bell nonlocality and quantum steering as well as Bayesian nets and causal inference.

We will discuss recent trapping and cooling experiments with optically levitated nanoparticles [1]. We will report on the cooling of all translational motional degrees of freedom of a single trapped silica particle to 1mK simultaneously at vacuum of 10-5 mbar using a parabolic mirror. We will further report on the squeezing of a thermal motional state of the trapped particle by rapid switching of the trap frequency [2]. 

We will further discuss ideas to experimentally test quantum mechanics by means of collapse models [3] by both matter-wave interferometry [4] and non-interferometric methods [5]. While first experimental bounds by non-interferometric tests have been achieved during the last year by a number of different experiments according to our idea [4], we at Southampton work on setting up the Nanoparticle Talbot Interferometer (NaTalI) to test the quantum superposition principle directly for one million atomic mass unit (amu) particles.

We will further discuss some ideas to probe the interplay between quantum mechanics and gravity by such levitated optomechanics experiments. One idea is to seek experimental evidence about the fundamentally quantum or classical nature of gravity by using the torsional motion of a non-spherical trapped particle [6], while a second idea is to test the effect of the gravity related shift of energy levels of the mechanical harmonic oscillator, which is predicted by semi-classical gravity (Schroedinger-Newton equation) [7] or thirdly try to pick up entanglement mediated by gravity [8].

We discuss the role of contextuality within quantum fluctuation theorems, in the light of a recent no-go result by Perarnau et al. We show that any fluctuation theorem reproducing the two-point measurement scheme for classical states either admits a notion of work quasi-probability or fails to describe protocols exhibiting contextuality.

Conversely, we describe a protocol that smoothly interpolates between the two-point measurement work distribution for projective measurements and Allahverdyan's work quasi-probability for weak measurements, and show that the negativity of the latter is a direct signature of contextuality.

Conventional quantum processes are described by quantum circuits, that represent evolutions of states of systems from input to output. In this seminar we consider transformations of an input circuit to an output circuit, which then represent the transformation of quantum evolutions. At this level, all the processes complying to admissibility conditions have in principle a physical realization scheme. The construction of a hierarchy of transformations of transformations, however, can proceed arbitrarily far, and in the higher orders one encounters admissible functions that have indefinite causal structures. These give rise to questions about possible realization schemes. Still, many of the maps in the hierarchy can be proved to have a realistic physical interpretation. In order to study the hierarchy, we introduce a simple rule for constructing new types of maps from known ones, and show how the tensor product can be rephrased in terms of the new rule. We use the hierarchy of types to introduce a partial order, which allows us to prove properties of maps by induction. We will then use induction proofs to discuss the characterisation of mathematically admissible maps at every level. We show an important structural result for a subclass of higher-order maps, and we conclude with the open question of their physical achievability.