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Uniform fields are one of the simplest and most pedagogically useful examples in introductory courses on electrostatics or Newtonian gravity. In general relativity there have been several proposals as to what constitutes a uniform field. In…
Non-relativistic quantum mechanics is reformulated here based on the idea that relational properties among quantum systems, instead of the independent properties of a quantum system, are the most fundamental elements to construct quantum…
Probabilistic Spacetime is a simple generalization of the classical model of spacetime in General Relativity, such that it allows to consider multiple metric field realizations endowed with probabilities. The motivation for such a…
Transitions of many-particle quantum systems between distinct phases at absolute-zero temperature, known as quantum phase transitions, require an exacting treatment of particle correlations. In this work, we present a general…
We define the model of quantum circuits with density matrices, where non-unitary gates are allowed. Measurements in the middle of the computation, noise and decoherence are implemented in a natural way in this model, which is shown to be…
The thesis concentrates on two problems in discrete geometry, whose solutions are obtained by analytic, probabilistic and combinatoric tools. The first chapter deals with the strong polarization problem. This states that for any sequence…
Simultaneous decoherence of conjugate observables of an open quantum system leads to a classical statistical mechanical description with constant phase space probability density in terms of a uniform ensemble. We investigate a scenario…
It has been recently suggested that probabilities of different events in the multiverse are given by the frequencies at which these events are encountered along the worldline of a geodesic observer (the "watcher"). Here I discuss an…
Exploiting photonic high-dimensional entanglement allows one to expand the bandwidth of quantum communication and information processing protocols through increased photon information capacity. However, the characterization of entanglement…
Convex sets of quantum states and processes play a central role in quantum theory and quantum information. Many important examples of convex sets in quantum theory are spectrahedra, that is, sets of positive operators subject to affine…
The measurement process in quantum mechanics is usually described by the von Neumann projection postulate, which forms a basic constituent of the laws of quantum mechanics. Since this postulate requires the outside observer of the system,…
The new Theorem on location of maximum of probability density functions of dimensionless second difference of the three adjacent energy levels for $N$-dimensional Gaussian orthogonal ensemble GOE($N$), $N$-dimensional Gaussian unitary…
The phase space of a relativistic system can be identified with the future tube of complexified Minkowski space. As well as a complex structure and a symplectic structure, the future tube, seen as an eight-dimensional real manifold, is…
We clarify different definitions of the density matrix by proposing the use of different names, the full density matrix for a single-closed quantum system, the compressed density matrix for the averaged single molecule state from an…
We review the Consistent Amplitude approach to Quantum Theory and argue that quantum probabilities are explicitly Bayesian. In this approach amplitudes are tools for inference. They codify objective information about how complicated…
We present a categorical viewpoint of probability measures by showing that a probability measure can be viewed as a weakly averaging affine measurable functional taking values in the unit interval which preserves limits. The probability…
How much can randomness help computation? Motivated by this general question and by volume computation, one of the few instances where randomness provably helps, we analyze a notion of dispersion and connect it to asymptotic convex…
This paper puts forward a new generalized polynomial dimensional decomposition (PDD), referred to as GPDD, comprising hierarchically ordered measure-consistent multivariate orthogonal polynomials in dependent random variables. Unlike the…
Let $p$ be a positive number. Consider probability measure $\gamma_p$ with density $\varphi_p(y)=c_{n,p}e^{-\frac{|y|^p}{p}}$. We show that the maximal surface area of a convex body in $\mathbb{R}^n$ with respect to $\gamma_p$ is…
The prepare-and-measure scenario offers the possibility to infer the dimension of an unknown physical system in a device-independent way, i.e. using only raw measurement data with apparatuses regarded as black boxes. We provide here a…