Quantum Foundations

While complex numbers are essential in mathematics, they are not needed to describe physical experiments, expressed in terms of probabilities, hence real numbers. Physics however aims to explain, rather than describe, experiments through theories. While most theories of physics are based on real numbers, quantum theory was the first to be formulated in terms of operators acting on complex Hilbert spaces. This has puzzled countless physicists, including the fathers of the theory, for whom a real version of quantum theory, in terms of real operators, seemed much more natural. Are complex numbers really needed in the quantum formalism? Here, we show this to be case by proving that real and complex quantum theory, understood in terms of operators in Hilbert spaces and tensor products to represent independent systems, make different predictions in network scenarios comprising independent states and measurements.  This allows us to devise a Bell-like experiment whose successful realization would disprove real quantum theory, in the same way as standard Bell experiments disproved local physics.

In absence of both experimental evidence for and a fully understood  theory of quantum gravity, the possibility that gravity might be  fundamentally classical presents an option to be considered. Such a  semiclassical theory also bears the potential to be part of an  objective explanation for the emergence of classical measurement outcomes. Nonetheless, the possibility is mostly disregarded based on the grounds of arguments of consistency. I will discuss these arguments, attempting to present the broader picture of the constraints that need to be dealt with in order to formulate consistent semiclassical models of gravity, and the implications this  has with regard to concrete proposals for theoretical models and 
experimental tests of semiclassical versus quantized gravity.

Zoom Link: https://pitp.zoom.us/j/99590707415?pwd=MHFMZlhSMUdMbFFoMEFmQTIxSUhBQT09

This talk is about how to think about probabilistic reasoning and its use in physics.  It has become commonplace, in the literature on the foundations of probability, to note that the word “probability” has been used in at least two distinct senses: an objective, physical sense (often called “objective chance”), thought to be characteristic of physical situations, independent of considerations of knowledge and ignorance, and an epistemic sense, having to do with gradations of belief of agents with limited information about the world.  I will argue that in order to do justice to the use of probabilistic concepts in physics, we should go beyond this familiar dichotomy, and make use of a third concept, which I call “epistemic chance,” which combines epistemic and physical considerations.

There are many different interpretations of quantum mechanics. Among them, QBism and Rovelli's Relational Quantum Mechanics (RQM) are special because they both propose that reality itself is produced relative to "observers". For QBism, observers are defined as rational decision-making "agents", while in RQM any physical system can be an observer. But both interpretations agree that reality is shaped by what happens when observers encounter the world external to themselves. In this talk I will try to understand what these interpretations imply for the ongoing problem of defining an ontological model of quantum mechanics.

A toy model due to Spekkens is constructed by applying an epistemic restriction to a classical theory but reproduces a host of phenomena that appear in quantum theory. The model advances the position that the quantum state may be interpreted as a reflection of an agent’s knowledge. However, the model fails to capture all quantum phenomena because it is non-contextual. Here we show how a theory similar to the one Spekkens proposes requires only a single augmentation to give quantum theory for certain systems. Specifically, one must combine all possible epistemically restricted classical accounts of a quantum experiment. The rule for combination is simple: sum the nonrandom parts of all classical predictions to arrive at the nonrandom part of the quantum prediction.

It is commonplace that quantum theory can be viewed as a ``non-classical" probability calculus. This observation has inspired the study of more general non-classical probabilistic theories modeled on QM, the so-called generalized probabilistic theories or GPTs. However, the boundary between these putatively non-classical probabilistic theories and classical probability theory is somewhat blurry, and perhaps even conventional. This is because, as is well known, any probabilistic model can be understood in classical terms if we are willing to embrace some form of contextuality. In this talk, I want to stress that this can often be done functorially: given a category $\Cat$ of probabilistic models, there are functors $F : \Cat \rightarrow \Set_{\Delta}$ where $\Set_{\Delta}$ is the category of sets and stochastic maps. In addition to the familiar Beltrametti-Bugajski representation, I'll exhibit two others that are less well known, one involving the ``semi-classical cover" and another, slightly more special, that allows one to represent a probabilistic model with sufficiently strong symmetry properties by a model having a completely classical probabilistic structure, in which any ``non-classicality" is moved into the dynamics, in roughly the spirit of Bohmian mechanics. 

(Based on http://philsci-archive.pitt.edu/16721/)

Zoom Link: https://pitp.zoom.us/j/91838172434?pwd=SUltOGlURWI5MDN6Qk45dnVRelBOQT09

The standard operational probabilistic framework (within which Quantum Theory can be formulated) is time asymmetric.  This is clear because the conditions on allowed operations include a time asymmetric causality condition.  This causality condition enforces that future choices do not influence past events.  To formulate operational theories in a time symmetric way I modify the basic notion of an operation allowing classical incomes as well as classical outcomes.  I provide a new time symmetric causality condition which I call double causality.  I apply these ideas to Quantum Theory proving, along the way, a time symmetric version of the Stinespring extension theorem using double causality.  I also propose the idea of a conditional frame of reference.  We can transform from the time symmetric frame of reference to a forward or a backward frame of reference.  This talk is based on arXiv:2104.00071.

We give a complete characterization of the (non)classicality of all stabilizer subtheories. First, we prove that there is a unique nonnegative and diagram-preserving quasiprobability representation of the stabilizer subtheory in all odd dimensions, namely Gross’s discrete Wigner function. This representation is equivalent to Spekkens’ epistemically restricted toy theory, which is consequently singled out as the unique noncontextual ontological model for the stabilizer subtheory. Strikingly, the principle of noncontextuality is powerful enough (at least in this setting) to single out one particular classical realist interpretation. Our result explains the practical utility of Gross’s representation, e.g. why (in the setting of the stabilizer subtheory) negativity in this particular representation implies generalized contextuality, and hence sheds light on why negativity of this particular representation is a necessary resource for universal quantum computation in the state injection model. This last fact, together with our result, implies that generalized contextuality is also a necessary resource for universal quantum computation in this model. In all even dimensions, we prove that there does not exist any nonnegative and diagram-preserving quasiprobability representation of the stabilizer subtheory, and, hence, that the stabilizer subtheory is contextual in all even dimensions.

Ontic structural realism is a form of scientific realism based on quantum mechanics in two ways:
(i) particles are not taken to be individual entities because they are not distinguishable; and, (ii) entanglement is taken to be relational structure that does not reduce to the state of parts and their causal interactions.

Furthermore, the idea of modal structure in OSR is exemplified by the way quantum mechanics sits between Bell-inequality violation and no-superluminal signalling. However, what should the advocate of OSR say about the measurement problem and decoherence? Wallace and Saunders combines OSR with Everettianism and argue that they need each other. Are Ladyman and Ross justified in their reluctance to agree with him?

Classical probabilistic models of quantum systems are not only relevant for understanding the non-classical features of quantum mechanics, but they are also useful for determining the possible advantage of using quantum resources for information processing tasks.  A common feature of these models is the presence of inaccessible information, as captured by the concept of preparation contextuality:  There are ensembles of quantum states described by the same density operator, and hence operationally indistinguishable, and yet in any probabilistic (ontological) model, they should be described by distinct probability distributions.  In this talk, I discuss a method for quantifying this inaccessible information and present a family of lower bounds on this quantity in terms of experimentally measurable quantities. These bounds, which can also be interpreted as a new class of robust non-contextuality inequalities, are obtained based on a family of guessing games.  As an application of this result, I derive a noise threshold for the presence of contextually in a noisy system, in terms of the average gate fidelity of the noise channel.

Experimental metaphysics is the study of how empirical results can reveal indisputable facts about the fundamental nature of the world, independent of any theory. It is a field born from Bell’s 1964 theorem, and the experiments it inspired, proving the world cannot be both local and deterministic. However, there is an implicit assumption in Bell’s theorem, that the observed result of any measurement is absolute (it has some value which is not ‘relative to its observer’). This assumption may be called into question when the observer becomes a quantum system (the “Wigner’s Friend” scenario), which has recently been the subject of renewed interest. Here, building on work by Brukner, we derive a theorem, in experimental metaphysics, for this scenario [1]. It is similar to Bell’s 1964 theorem but dispenses with the assumption of determinism. The remaining assumptions, which we collectively call "local friendliness", yield a strictly larger polytope of bipartite correlations than those in Bell's theorem (local determinism), but quantum mechanics still allows correlations outside the local friendliness polytope.  We illustrate this in an experiment in which the friend system is a single photonic qubit [1]. I argue that a truly convincing experiment could be realised if that system were a sufficiently advanced artificial intelligence software running on a very large quantum computer, so that it could be regarded genuinely as a friend. I will briefly discuss the implications of this far-future scenario for various interpretations and modifications of quantum theory.

[1] Kok-Wei Bong, Aníbal Utreras-Alarcón, Farzad Ghafari, Yeong-Cherng Liang, Nora Tischler, Eric G. Cavalcanti, Geoff J. Pryde and Howard M. Wiseman, “A strong no-go theorem on the Wigner’s friend paradox", Nature Physics (2020).