Quantum Foundations

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.

Seven years ago, the first paper was published [1] on what has come to be known as the “Many Interacting Worlds” (MIW) interpretation of quantum mechanics (QM) [2,3,4]. MIW is based on a new formulation of QM [1,5,6], in which the wavefunction Ψ(t, x) is discarded entirely. Instead, the quantum state is represented as an ensemble, x(t, C), of quantum trajectories or “worlds.” Each of these worlds has well-defined real-valued particle positions and momenta, and is thereby classical-like. Unlike a classical ensemble, however, nearby trajectories/worlds can interact with each other dynamically, giving rise to quantum effects. In this respect, MIW is very different from the Everett Many-Worlds Interpretation (MWI); another key difference is that no world branching occurs.

The MIW approach offers a direct “realist” description of nature that may be beneficial in interpreting quantum phenomena such as entanglement, measurement, spontaneous decay, etc. It provides a useful analysis of MWI, explaining how the illusion of world branching emerges in that context. Moreover, x(t, C) satisfies a trajectory-based action principle, which allows quantum theory (via the Euler-Lagrange equation and Noether’s theorem) to be placed on the same footing as classical theories. In this manner, a straightforward relativistic generalization can also be obtained [7,8], which offers a notion of global simultaneity even for accelerating observers. Whereas the original MIW theory is fully consistent with Schroedinger wave mechanics, the more recently developed flavors offer the promise of new experimental predictions. These and other developments, e.g. for many dimensions, multiple particles, and spin, may also be discussed.

[1] B. Poirier, Chem. Phys. 370, 4 (2010).
[2] M. J. W. Hall, D.-A. Deckert, and H. Wiseman, Phys. Rev. X 4, 041013 (2014)
[3] B. Poirier, Phys. Rev. X, 4, 040002 (2014).
[4] C. T. Sebens, Phil. Sci. 82, 266 (2015).
[5] P. Holland, Ann. Phys. 315, 505 (2005).
[6] J. Schiff and B. Poirier, J. Chem. Phys. 136, 031102 (2012).
[7] B. Poirier, arXiv:1208.6260 [quant-ph], (2012).
[8] H.-M. Tsai and B. Poirier, EmQM15: Emergent Quantum Mechanics 2015, ed. G. Grössing, (J. Physics, IOP, 2016) 701, 012013.

The path integral formulation of quantum mechanics has been immensely influential, particularly in high energy physics. However, its applications to quantum circuits has so far been more limited. In this talk I will discuss the sum-over-paths approach to computing transition amplitudes in Clifford circuits. In such a formulation, the relative phases of different discrete-time paths through the configuration space can be defined in terms of a classical action which is provided by the discrete Wigner representation. As an application of the sum-over-paths technique I will show how to recover a version of the Gottesman-Knill theorem, namely that the transition amplitudes in Clifford circuits can be computed efficiently.

Device-independent self-testing allows user to identify the measured quantum states and the measurements made in a device using the observed statistics. Such verification scheme only requires assuming the validity of quantum theory and no-signalling. As such, no assumptions are required about the inner-workings of the device. Hence, self-testing allows laymen to test the serviceability of a quantum device without needing its blueprint. This talk will be primarily focused on the self-testing of bipartite entangled pure states [Nat. Comms. 8, 15485 (2017)]. Also, I will be touching on the recent study of the geometry of the quantum set [In preparation].

What can machine learning teach us about quantum mechanics? I will begin with a brief overview of attempts to bring together the two fields, and the insights this may yield. I will then focus on one particular framework, Projective Simulation, which describes physics-based agents that are capable of learning by themselves. These agents can serve as toy models for studying a wide variety of phenomena, as I will illustrate with examples from quantum experiments and biology.

We construct a hidden variable model for the EPR correlations using a Restricted Boltzmann Machine. The model reproduces the expected correlations and thus violates the Bell inequality, as required by Bell's theorem. Unlike most hidden-variable models, this model does not violate the locality assumption in Bell's argument. Rather, it violates measurement independence, albeit in a decidedly non-conspiratorial way.

In this talk I am going to describe Spekkens’ toy model, a non-contextual hidden variable model with an epistemic restriction, a constraint on what an observer can know about reality. The aim of the model, developed for continuous and discrete prime degrees of freedom, is to advocate the epistemic view of quantum theory, where quantum states are states of incomplete knowledge about a deeper underlying reality. In spite of its classical flavour, many aspects that were thought to belong only to quantum mechanics can be reproduced in the model. 

I am going to describe our results regarding the formulation of rules for the update of states after measurement. I will do it for systems of discrete prime dimensions and I will then give the idea on how to proceed in the non-prime dimensional case. 

I will also depict the relationship between Spekkens’ model, stabiliser quantum mechanics and Gross' theory of discrete Wigner functions (they are equivalent theories in odd dimensions) in terms of measurement update rules.

I will conclude by briefly discussing a project we have been recently working on that consists of characterising sub theories of Spekkens’ model that are operationally equivalent to sub theories of QM (in particular in the case of qubits) and use them to represent the non-contextual classically simulable part of state-injection schemes of computation with contextuality as a resource.