Related papers: Complexity in Tame Quantum Theories
State transformation problems such as compressing quantum information or breaking quantum commitments are fundamental quantum tasks. However, their computational difficulty cannot easily be characterized using traditional complexity theory,…
In this article we present a possible way to make usual quantum mechanics fully compatible with physical realism, defined as the statement that the goal of physics is to study entities of the natural world, existing independently from any…
Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilistic theories exist which all share some…
Based on ideas of quantum theory of open systems we propose the consistent approach to the formulation of logic of plausible propositions. To this end we associate with every plausible proposition diagonal matrix of its likelihood and…
An interpretation and re-formulation of modern physics which removes the presumption of the space-time continuum, and bases physical theory on a small number of rational and empirical principles. After briefly describing the philosophical…
We consider the problem of quantum behavior in the finite background. Introduction of continuum or other infinities into physics leads only to technical complications without any need for them in description of empirical observations. The…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…
We give a basic overview of computational complexity, query complexity, and communication complexity, with quantum information incorporated into each of these scenarios. The aim is to provide simple but clear definitions, and to highlight…
Computational complexity theory contains a corpus of theorems and conjectures regarding the time a Turing machine will need to solve certain types of problems as a function of the input size. Nature {\em need not} be a Turing machine and,…
A "minimal" generalization of Quantum Mechanics is proposed, where the Lagrangian or the action functional is a mapping from the (classical) states of a system to the Lie algebra of a general compact Lie group, and the wave function takes…
The future development of quantum technologies relies on creating and manipulating quantum systems of increasing complexity, with key applications in computation, simulation and sensing. This poses severe challenges in the efficient…
Several finite dimensional quasi-probability representations of quantum states have been proposed to study various problems in quantum information theory and quantum foundations. These representations are often defined only on restricted…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by being based on two…
A set of general physical principles is proposed as the structural basis for the theory of complex systems. First the concept of harmony is analyzed and its different aspects are uncovered. Then the concept of reflection is defined and…
We present an information-theoretic interpretation of quantum formalism based on a Bayesian framework and devoid of any extra axiom or principle. Quantum information is construed as a technique for analyzing a logical system subject to…
Underlying any theory of physics is a layer of conceptual frames. They connect the mathematical structures used in theoretical models with physical phenomena, but they also constitute our fundamental assumptions about reality. Many of the…
The o-minimal structure generated by the restricted Pfaffian functions, known as restricted sub-Pfaffian sets, admits a natural measure of complexity in terms of a format $\mathcal{F}$, recording information like the number of variables and…
Topos theory, a branch of category theory, has been proposed as mathematical basis for the formulation of physical theories. In this article, we give a brief introduction to this approach, emphasising the logical aspects. Each topos serves…
The ultimate limits of computation are not just logical, but physical. We investigate the physical resources -- time, energy, entropy, and free energy -- required to perform computational work. We apply the resulting measures of physical…
It is the matter of fact that quantum mechanics operates with notions that are not determined in the frame of the mechanics' formalism. Among them we can call the notion of "wave-particle" (that, however, does not appear in both classical…