Related papers: Symmetry and composition in probabilistic theories
Probabilistic programming is related to a compositional approach to stochastic modeling by switching from discrete to continuous time dynamics. In continuous time, an operator-algebra semantics is available in which processes proceeding in…
These notes review a description of quantum mechanics in terms of the topology of spaces, basing on the axioms of Topological Quantum Field Theory and path integral formalism. In this description quantum states and operators are encoded by…
Quantum supermaps provide a framework in which higher order quantum processes can act on lower order quantum processes. In doing so, they enable the definition and analysis of new quantum protocols and causal structures. Recently, key…
Quantum gates built out of braid group elements form the building blocks of topological quantum computation. They have been extensively studied in $SU(2)_k$ quantum group theories, a rich source of examples of non-Abelian anyons such as the…
Motivated by Quantum Bayesianism I give background for a general epistemic approach to quantum mechanics, where complementarity and symmetry are the only essential features. A general definition of a symmetric epistemic setting is…
Quantum theory provides a significant example of two intermingling hallmarks of science: the ability to consistently combine physical systems and study them compositely, and the power to extract predictions in the form of correlations. A…
The ability to control quantum systems using shaped fields as well as to infer the states of such controlled systems from measurement data are key tasks in the design and operation of quantum devices. Here we associate the success of…
The main ideas behind nuclear supersymmetry are presented, starting from the basic concepts of symmetry and the methods of group theory in physics. We propose new, more stringent experimental tests that probe the supersymmetry…
Quantum mechanical systems with some degree of complexity due to multiple scattering behave as if their Hamiltonians were random matrices. Such behavior, while originally surmised for the interacting many-body system of highly excited…
Bootstrap methods, initially developed for solving statistical and quantum field theories, have recently been shown to capture the discrete spectrum of quantum mechanical problems, such as the single particle Schr\"odinger equation with an…
Complementarity relations between various characterizations of a probability distribution are at the core of information theory. In particular, lower and upper bounds for the entropic function are of great importance. In applied topics, we…
A core level of basic information for physics is identified, based on an analysis of the characteristics of the parameters space, time, mass and charge. At this level, it is found that certain symmetries operate, which can be used to…
The aim of this review is to present and analyze the probabilistic models of mathematical phylogenetics which have been intensively used in recent years in biology as the cornerstone of attempts to infer and reconstruct the ancestral…
We reconstruct quantum theory starting from the premise that, as Asher Peres remarked, "Unperformed experiments have no results." The tools of modern quantum information theory, and in particular the symmetric informationally complete (SIC)…
Techniques from higher categories and higher-dimensional rewriting are becoming increasingly important for understanding the finer, computational properties of higher algebraic theories that arise, among other fields, in quantum…
We describe a cohomological framework for measurement based quantum computation, in which symmetry plays a central role. Therein, the essential information about the computational output is contained in topological invariants, namely…
We prove sufficient conditions for Topological Quantum Order at both zero and finite temperatures. The crux of the proof hinges on the existence of low-dimensional Gauge-Like Symmetries (that notably extend and differ from standard local…
The relativistic two-particle quantum mixtures are studied from the topological point of view. The mixture field variables can be transformed in such a way that a kinematical decoupling of both particle degrees of freedom takes place with a…
There is a long history of representing a quantum state using a quasi-probability distribution: a distribution allowing negative values. In this paper we extend such representations to deal with quantum channels. The result is a convex,…
The composite particle duality extends the notions of both flux attachment and statistical transmutation in spacetime dimensions beyond 2+1D. It constitutes an exact correspondence that can be understood either as a theoretical framework or…