Related papers: Quantization Rules for Dynamical Systems

The Principle of Complementarity of Probabilities based on of noncommutative probability is introduced.

We demonstrate the possibility of classifying causal systems into kinds that share a common structure without first constructing an explicit dynamical model or using prior knowledge of the system dynamics. The algorithmic ability to…

Recently, an interesting form of non-classical effect which can be considered as a form of contextuality within quantum mechanics, has been demonstrated for a four-level system by discriminating the different routes that are taken for…

Model quantization, which aims to compress deep neural networks and accelerate inference speed, has greatly facilitated the development of cumbersome models on mobile and edge devices. There is a common assumption in quantization methods…

We propose a method of quantization based on Hamilton-Jacobi theory in the presence of a random constraint due to the fluctuations of a set of hidden random variables. Given a Lagrangian, it reproduces the results of canonical quantization…

We discuss the process to obtain Poisson brackets among the phase-space variables of a system of a charged particle on a Poincar\'e hyperboloid in the presence of a uniform magnetic field. We show that after quantization the Dirac bracket…

The ``generic'' family of classical sequential growth dynamics for causal sets provides cosmological models of causal sets which are a testing ground for ideas about the, as yet unknown, quantum theory. In particular we can investigate how…

Using arbitrary symplectic structures and parametrization invariant actions, we develop a formalism, based on Dirac's quantization procedure, that allows us to consider theories with both space-space as well as space-time noncommutativity.…

We study the problem of selecting covariates for unbiased estimation of the total causal effect.Existing approaches typically rely on global causal structure learning over all variables, or on strong assumptions such as causal sufficiency -…

In this thesis we investigate the importance of causality in non-perturbative approaches to quantum gravity. Firstly, causal sets are introduced as a simple kinematical model for causal geometry. It is shown how causal sets could account…

Causal discovery methods seek to identify causal relations between random variables from purely observational data, as opposed to actively collected experimental data where an experimenter intervenes on a subset of correlates. One of the…

Free noncommutative fields constitute a natural and interesting example of constrained theories with higher derivatives. The quantization methods involving constraints in the higher derivative formalism can be nicely applied to these…

We focus on variational inference in dynamical systems where the discrete time transition function (or evolution rule) is modelled by a Gaussian process. The dominant approach so far has been to use a factorised posterior distribution,…

Structural equation models and Bayesian networks have been widely used to analyze causal relations between continuous variables. In such frameworks, linear acyclic models are typically used to model the datagenerating process of variables.…

Conventionally the total correlations within a quantum system are quantified through distance-based expressions such as the relative entropy or the square-norm. Those expressions imply that a quantum state can contain both classical and…

This paper presents an brief review of some recent work on the causal set approach to quantum gravity. Causal sets are a discretisation of spacetime that allow the symmetries of GR to be preserved in the continuum approximation. One…

Within a general operational framework I show that a-causality at a distance of "local actions" (the so-called "no-signaling") is a direct consequence of commutativity of local transformations, i.e. of dynamical independence. On the other…

We derive a framework for quantifying entanglement in multipartite and high dimensional systems using only correlations in two unbiased bases. We furthermore develop such bounds in cases where the second basis is not characterized beyond…

The first goal of this paper is to show that discreteness, locality, and relativistic covariance can peacefully coexist if the ordinary spacetime (OST) is replaced with phase spacetime (PST) as a geometric background of a Poisson process,…

We present a novel derivation of special relativity based on the information physics of events comprising a causal set. We postulate that events are fundamental, and that some events have the potential to receive information about other…