相关论文: A Royal Road to Quantum Theory (or Thereabouts), E…

This paper fails to derive quantum mechanics from a few simple postulates. But it gets very close --- and it does so without much exertion. More exactly, I obtain a representation of finite-dimensional probabilistic systems in terms of…

We consider possible non-signaling composites of probabilistic models based on euclidean Jordan algebras. Subject to some reasonable constraints, we show that no such composite exists having the exceptional Jordan algebra as a direct…

Quantum bits can be isolated to perform useful information-theoretic tasks, even though physical systems are fundamentally described by very high-dimensional operator algebras. This is because qubits can be consistently embedded into…

This note adds to the recent spate of derivations of the probabilistic apparatus of finite-dimensional quantum theory from various axiomatic packages. We offer two different axiomatic packages that lead easily to the Jordan algebraic…

Using a result of H. Hanche-Olsen, we show that (subject to fairly natural constraints on what constitutes a system, and on what constitutes a composite system), orthodox finite-dimensional complex quantum mechanics with superselection…

This paper offers a brief introduction to the framework of "general probabilistic theories", otherwise known as the "convex-operational" approach the foundations of quantum mechanics. Broadly speaking, the goal of research in this vein is…

I explore several related routes to deriving the Jordan-algebraic structure of finite-dimensional quantum theory from more transparent operational or physical principles, mainly involving ideas about the symmetries of, and the correlations…

We define symmetric spaces in arbitrary dimension and over arbitrary non-discrete topological fields $\K$, and we construct manifolds and symmetric spaces associated to topological continuous quasi-inverse Jordan pairs and -triple systems.…

We consider possible non-signaling composites of probabilistic models based on euclidean Jordan algebras (EJAs), satisfying some reasonable additional constraints motivated by the desire to construct dagger-compact categories of such…

We show how to formulate physical theory taking as a starting point the set of states (geometric approach). We discuss the relation of this formulation to the conventional approach to classical and quantum mechanics and the theory of…

Symmetry postulates play a crucial role in various approaches to reconstruct quantum theory from a few basic principles. Discrete and continuous symmetries are under consideration. The continuous case better matches the physical needs for…

Presentations of categories are a well-known algebraic tool to provide descriptions of categories by means of generators, for objects and morphisms, and relations on morphisms. We generalize here this notion, in order to consider situations…

We develop a theory of quantum sufficiency on real *-subalgebras and real Jordan algebras. In contrast to the conventional formulation, which is based on families of states, complex completely positive coarse-grainings, and Radon-Nikodym…

Most quantum logics do not allow for a reasonable calculus of conditional probability. However, those ones which do so provide a very general and rich mathematical structure, including classical probabilities, quantum mechanics as well as…

Physical theories can be characterized in terms of their state spaces and their evolutive equations. The kinematical structure and the dynamical structure of finite dimensional quantum theory are, in light of the Choi-Jamio{\l}kowski…

We develop a version of quantum mechanics that can handle nonassociative algebras of observables and which reduces to standard quantum theory in the traditional associative setting. Our algebraic approach is naturally probabilistic and is…

While real Hamiltonian mechanics and Hermitian quantum mechanics can both be cast in the framework of complex canonical equations, their complex generalisations have hitherto been remained tangential. In this paper quaternionic and…

The Jordan structure of finite-dimensional quantum theory is derived, in a conspicuously easy way, from a few simple postulates concerning abstract probabilistic models (each defined by a set of basic measurements and a convex set of…

Quantum theory's Hilbert space apparatus in its finite-dimensional version is nearly reconstructed from four simple and quantum-mechanically motivated postulates for a quantum logic. The reconstruction process is not complete, since it…

We apply the quaternionic Jordan form to classify the hypercomplex nilpotent almost abelian Lie algebras in all dimensions and to carry out the complete classification of 12-dimensional hypercomplex almost abelian Lie algebras. Moreover, we…