Quantum Foundations

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.

Quantum gravity has many conceptual problems. Amongst the most well-known is the "Problem of Time": gravitational observables are global in time, while we would really like to obtain probabilities for processes taking us from an observable at one time to another, later one. Tackling these questions using relationalism will be the preferred strategy during this talk. The 'relationalist' approach leads us to shed much redundant information and enables us to identify a reduced configuration space as the arena on which physics unfolds, a goal still beyond our reach in general relativity. Moreover, basing our ontology on this space has far-reaching consequences. One is that it suggests a natural interpretation of quantum mechanics; it is a form of ‘Many-Worlds’ called Many-Instant QM. Another is that the gravitational reduced configuration space has a rich, highly asymmetric structure which singles out preferred, non-singular and homogeneous initial conditions for a wave-function of the universe, which is yet to be explored.   

Quantum mechanics can be seen as a set of instructions how to calculate probabilities by associating mathematical objects to physical procedures, like preparation, manipulation, and measurement of a system. Quantum theory then yields probabilities which are neutral with respect to its use, e.g., in a Bayesian or a frequentistic way. We investigate a different approach to quantum theory and physical theories in general, in which we aim for subjective predictions in the Bayesian sense. This gives a structure different from the operational framework of general probabilistic theories. We explore these differences and the according mathematical language of such probabilistic Bayesian theories. This is joint work with Adan Cabello, Giulio Chiribela, and Markus Müller.