Related papers: Combining Determinism and Indeterminism
The concept of randomized measurements on individual particles has proven to be useful for analyzing quantum systems and is central for methods like shadow tomography of quantum states. We introduce $\textit{collective}$ randomized…
Quantum computing provides a powerful framework for tackling computational problems that are classically intractable. The goal of this paper is to explore the use of quantum computers for solving relevant problems in systems and control…
Given a differential equation with infinite-dimensional symmetry pseudo-group it is shown, using an example, that it is generally not possible to construct enough joint invariants to form an invariant numerical scheme of the equation. To…
We advance a Bayesian concept of 'intrinsic asymptotic universality' taking to its final conclusions previous conceptual and numerical work based upon a concept of a reprogrammability test and an investigation of the complex qualitative…
We identify computability-theoretic properties enabling us to separate various statements about partial orders in reverse mathematics. We obtain simpler proofs of existing separations, and deduce new compound ones. This work is part of a…
We outline the construction of a molecular system that could, in principle, implement a thermodynamically reversible Universal Turing Machine (UTM). By proposing a concrete-albeit idealised-design and operational protocol, we reveal…
Predictions for measurement outcomes in physical theories are usually computed by combining two distinct notions: a state, describing the physical system, and an observable, describing the measurement which is performed. In quantum theory,…
We give a mathematical definition for the notion of inconclusive quantum measurements. In physics, such measurements occur at intermediate stages of a complex measurement procedure, with the final measurement result being operationally…
Treating the time of an event as a quantum variable, we derive a scheme in which superpositions in time are used to perform operations in an indefinite causal order. We use some aspects of a recently developed space-time-symmetric formalism…
The rapid development of derandomization theory, which is a fundamental area in theoretical computer science, has recently led to many surprising applications outside its initial intention. We will review some recent such developments…
The main objective of this paper is the following two results. (1) There exists a computable bi-orderable group that does not have a computable bi-ordering; (2) There exists a bi-orderable, two-generated recursively presented solvable group…
This work lies in the fusion of experimental economics and data mining. It continues author's previous work on mining behaviour rules of human subjects from experimental data, where game-theoretic predictions partially fail to work.…
Many different definitions of computational universality for various types of dynamical systems have flourished since Turing's work. We propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical…
The theory of noninterference supports the analysis of secure computations in multi-level security systems. Classical equivalence-based approaches to noninterference mainly rely on bisimilarity. In a nondeterministic setting, assessing…
This paper presents a theory of systemic undecidability, reframing incomputability as a structural property of systems rather than a localized feature of specific functions or problems. We define a notion of causal embedding and prove a…
By means of a digit function that has been introduced in a recent formulation of classical and quantum mechanics, we provide a new construction of some infinite families of finite groups, both abelian and nonabelian, of importance for…
In recent work, Benjamin Schumacher and Michael~D. Westmoreland investigate a version of quantum mechanics which they call "modal quantum theory" but which we prefer to call "discrete quantum theory". This theory is obtained by…
Semigroup theory is a branch of abstract algebra, and it provides mathematical tools for the theory of computation. Finite semigroups can describe state transition systems and thus they model physically realizable computers. Engineering…
Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and…
The search for meaningful structure in biological data has relied on cutting-edge advances in computational technology and data science methods. However, challenges arise as we push the limits of scale and complexity in biological problems.…