Related papers: A convergent inflation hierarchy for quantum causa…
The Glivenko-Cantelli theorem states that the empirical distribution function converges uniformly almost surely to the theoretical distribution for a random variable $X \in \mathbb{R}$. This is an important result because it establishes the…
We consider the problem of approximating partition functions for Ising models. We make use of recent tools in combinatorial optimization: the Sherali-Adams and Lasserre convex programming hierarchies, in combination with variational methods…
Causal modelling is a tool for generating causal explanations of observed correlations and has led to a deeper understanding of correlations in quantum networks. Existing frameworks for quantum causality tend to focus on acyclic causal…
We investigate the global structure of inflationary universe both by analytical methods and by computer simulations of stochastic processes in the early Universe. We show that the global structure of the universe depends crucially on the…
The particle production process is reviewed, through which cosmic inflation can produce a scale invariant superhorizon spectrum of perturbations of suitable fields starting from their quantum fluctuations. Afterwards, in the context of the…
Ideally, all analyses of normally distributed data should include the full covariance information between all data points. In practice, the full covariance matrix between all data points is not always available. Either because a result was…
An operational probabilistic theory where all systems are classical, and all pure states of composite systems are entangled, is constructed. The theory is endowed with a rule for composing an arbitrary number of systems, and with a…
Cosmological perturbations generated during inflation exhibit striking quantum features, including entanglement and high circuit complexity. Yet their observational signatures remain effectively indistinguishable from classical stochastic…
Bell's Theorem shows that quantum mechanical correlations can violate the constraints that the causal structure of certain experiments impose on any classical explanation. It is thus natural to ask to which degree the causal assumptions --…
In spite of the macroscopic character of the fluctuation amplitudes, we show that the standard inflationary distribution of primordial density fluctuations still exhibits inherently quantum mechanical correlations (which cannot be mimicked…
The most robust prediction of inflationary cosmology is the existence of a red tilt for the spectrum of curvature fluctuations that is experimentally of order $0.04$. The tilt is derived solving the exact equation for quantum fluctuations…
A quantum algorithm for general combinatorial search that uses the underlying structure of the search space to increase the probability of finding a solution is presented. This algorithm shows how coherent quantum systems can be matched to…
A finite form of de Finetti's representation theorem is established using elementary information-theoretic tools: The distribution of the first $k$ random variables in an exchangeable binary vector of length $n\geq k$ is close to a mixture…
Existing work on quantum causal structure assumes that one can perform arbitrary operations on the systems of interest. But this condition is often not met. Here, we extend the framework for quantum causal modelling to situations where a…
In scientific inference problems, the underlying statistical modeling assumptions have a crucial impact on the end results. There exist, however, only a few automatic means for validating these fundamental modelling assumptions. The…
This paper proposes a causal inference relation and causal programming as general frameworks for causal inference with structural causal models. A tuple, $\langle M, I, Q, F \rangle$, is an instance of the relation if a formula, $F$,…
Causal consistency is one of the most adopted consistency criteria for distributed implementations of data structures. It ensures that operations are executed at all sites according to their causal precedence. We address the issue of…
Testing whether a probability distribution is compatible with a given Bayesian network is a fundamental task in the field of causal inference, where Bayesian networks model causal relations. Here we consider the class of causal structures…
The stochastic inflation program is a framework for understanding the dynamics of a quantum scalar field driving an inflationary phase. Though widely used and accepted, there have over recent years been serious criticisms of this theory. In…
In the standard inflationary paradigm the inhomogeneities observed in the CMB arise from quantum fluctuations of an initially homogeneous and isotropic vacuum state. This picture suffers from two well-known weaknesses. First, it assumes…