Related papers: Quantum computation with indefinite causal structu…
We present an original model of paraconsistent Turing machines (PTMs), a generalization of the classical Turing machines model of computation using a paraconsistent logic. Next, we briefl y describe the standard models of quantum…
Understanding quantum theory's causal structure stands out as a major matter, since it radically departs from classical notions of causality. We present advances in the research program of causal decompositions, which investigates the…
Quantum computing promises exponential improvements in solving large systems of partial differential equations (PDE), which forms a bottleneck in high-resolution computational fluid dynamics (CFD) simulations, in, among others, aerospace…
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…
One-way measurement based quantum computations (1WQC) may describe unitary transformations, via a composition of CPTP maps which are not all unitary themselves. This motivates the following decision problems: Is it possible to determine…
There is good evidence that quantum computers are more powerful than classical computers, and that various simple modifications of quantum theory yield computational power that is dramatically greater still. However, these modifications…
A recent framework of quantum theory with no global causal order predicts the existence of "causally nonseparable" processes. Some of these processes produce correlations incompatible with any causal order (they violate so-called "causal…
The possible existence of closed timelike curves (CTCs) draws attention to fundamental questions about what is physically possible and what is not. An example is the "no cloning theorem" in quantum mechanics, which states that no physical…
Predictive coding has emerged as an influential normative model of neural computation, with numerous extensions and applications. As such, much effort has been put into mapping PC faithfully onto the cortex, but there are issues that remain…
General definitions for causal structures on manifolds of dimension d+1>2 are presented for the topological category and for any differentiable one. Locally, these are given as cone structures via local (pointwise) homeomorphic or…
It has been shown that it is theoretically possible for there to exist quantum and classical processes in which the operations performed by separate parties do not occur in a well-defined causal order. A central question is whether and how…
Deep generative models have shown tremendous capability in data density estimation and data generation from finite samples. While these models have shown impressive performance by learning correlations among features in the data, some…
Research on indefinite causal structures is a rapidly evolving field that has a potential not only to make a radical revision of the classical understanding of space-time but also to achieve enhanced functionalities of quantum information…
We examine consequences of the density matrix approach to quantum theory in the context of a model spacetime containing closed timelike curves and find that in general, an initially pure state will evolve in a nonlinear way to a mixed…
Causal analyses of longitudinal data generally assume that the qualitative causal structure relating variables remains invariant over time. In structured systems that transition between qualitatively different states in discrete time steps,…
We expect a theory of Quantum Gravity to be both probabilistic and have indefinite causal structure. Indefinite causal structure poses particular problems for theory formulation since many of the core ideas used in the usual approaches to…
Existing approaches to causal discovery often rely on restrictive modeling assumptions that limit their applicability in real-world settings, particularly when data are heavy-tailed or contain a mixture of discrete and continuous variables.…
Quantum field theory (QFT) in classical spacetime has revealed interesting and puzzling aspects about gravitational systems, in particular black hole thermodynamics and its information processing. Although quantum gravitational effects may…
Many fundamental and key objects in quantum mechanics are linear mappings between particular affine/linear spaces. This structure includes basic quantum elements such as states, measurements, channels, instruments, non-signalling channels…
This paper argues that the requirement of applicableness of quantum linearity to any physical level from molecules and atoms to the level of macroscopic extensional world, which leads to a main foundational problem in quantum theory…