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Inferring the causal structure that links n observables is usually based upon detecting statistical dependences and choosing simple graphs that make the joint measure Markovian. Here we argue why causal inference is also possible when only…
This paper presents an elementary introduction to Consistent Quantum Theory (CQT), as developed by Griffiths and others over the past 25 years. The theory is a version of orthodox(Copenhagen) quantum mechanics, based on the notion that the…
We prove general de Finetti type theorems for classical and free independence. The de Finetti type theorems work for all non-easy quantum groups, which generalize a recent work of Banica, Curran and Speicher. We determine maximal…
This thesis is dedicated to studying cosmological inflation, which is a period of accelerated expansion in the very early Universe that is required to explain the observed anisotropies in the cosmic microwave background. Inflation, when…
We are on the verge of the first precision testing of the inflationary cosmology as a model for the origin of structure in the Universe. I review the key predictions of inflation which can be used as observational tests, in the sense of…
Quantum collision models normally consist of a system interacting with a set of ancillary units representing the environment. While these ancillary systems are usually assumed to be either two level systems (TLS) or harmonic oscillators, in…
Reversible computation is key in developing new, energy-efficient paradigms, but also in providing forward-only concepts with broader definitions and finer frames of study.Among other fields, the algebraic specification and representation…
Thermal behavior in subsystems of closed quantum systems is commonly attributed to dynamical chaos, quantum ergodicity, canonical typicality, or the eigenstate thermalization hypothesis, suggesting a fundamentally statistical origin of…
It is sometimes argued that observation of tensor modes from inflation would provide the first evidence for quantum gravity. However, in the usual inflationary formalism, also the scalar modes involve quantised metric perturbations. We…
Measurement incompatibility is the most basic resource that distinguishes quantum from classical physics. Contextuality is the critical resource behind the power of some models of quantum computation and is also a necessary ingredient for…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
Statistical sufficiency formalizes the notion of data reduction. In the decision theoretic interpretation, once a model is chosen all inferences should be based on a sufficient statistic. However, suppose we start with a set of procedures…
Since the advent of inflation, several theorems have been proven suggesting that although inflation can (and generically does) continue eternally into the future, it cannot be extended eternally into the past to create a ``steady-state''…
Inflation is most often described using quantum field theory (QFT) on a fixed, curved spacetime background. Such a description is valid only if the spatial volume of the region considered is so large that its size and shape moduli behave…
Deviations from classical physics when distant quantum systems become correlated are interesting both fundamentally and operationally. There exist situations where the correlations enable collaborative tasks that are impossible within the…
The space of inflationary models is vast, containing wide varieties of mechanisms, symmetries, and spectra of particles. Consequently, the space of observational signatures is similarly complex. Hence, it is natural to look for boundaries…
We prove a de Finetti theorem for exchangeable sequences of states on test spaces, where a test space is a generalization of the sample space of classical probability theory and the Hilbert space of quantum theory. The standard classical…
We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global…
While clustering is ubiquitously used across science and industry, uncertainty in cluster assignments is rarely quantified with rigorous guarantees. We propose a novel conformal inference framework for clustering that returns confidence…
The inflationary paradigm is an important cornerstone of the concordance cosmological model. However, standard inflation cannot fully address the transition from an early homogeneous and isotropic stage, to another one lacking such…