Related papers: Symmetry, model reduction, and quantum mechanics
We first review and critically examine some basic concepts and ambiguities related to quantum mechanics and quantum measurement to understand the success and shortcomings of current theories. We also touch on ideas regarding expression of…
In any given experimental scenario, the rules of quantum theory provide statistical distributions that the observed outcomes are expected to follow. The set formed by all these distributions contains the imprint of quantum theory, capturing…
Symmetry is an important property of quantum mechanical systems which may dramatically influence their behavior in and out of equilibrium. In this paper, we study the effect of symmetry on tripartite entanglement properties of typical…
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…
So far, none of attempts to quantize gravity has led to a satisfactory model that not only describe gravity in the realm of a quantum world, but also its relation to elementary particles and other fundamental forces. Here, we outline the…
A composite quantum system comprising a finite number k of subsystems which are described with position and momentum variables in Z_{n_{i}}, i=1,...,k, is considered. Its Hilbert space is given by a k-fold tensor product of Hilbert spaces…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
We work out a classification scheme for quantum modeling in Hilbert space of any kind of composite entity violating Bell's inequalities and exhibiting entanglement. Our theoretical framework includes situations with entangled states and…
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…
We present a general approach to quantum entanglement and entropy that is based on algebras of observables and states thereon. In contrast to more standard treatments, Hilbert space is an emergent concept, appearing as a representation…
We show that when non-commutative quantum mechanics is formulated on the Hilbert space of Hilbert-Schmidt operators (referred to as quantum Hilbert space) acting on a classical configuration space, spectral triplets as introduced by Connes…
In Quantum Physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties…
It is shown that the quantum theory can be formulated on homogeneous spaces of generalized coherent states in a manner that accounts for interference, entanglement, and the linearity of dynamics without using the superposition principle.…
A quantum system can be entirely described by the K\"ahler structure of the projective space P(H) associated to the Hilbert space H of possible states; this is the so-called geometrical formulation of quantum mechanics. In this paper, we…
In the book [4] the general problem of reconstructing the Hilbert space formulation in quantum theory is discussed from the point of view of what I called conceptual variables, any variables defined by a person or by a group of persons.…
Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space. This is well known and it usually proceeds by partitioning…
Five physical assumptions are proposed that together entail the general qualitative results, including the Born rule, of non-relativistic quantum mechanics by physical and information-theoretic reasoning alone. Two of these assumptions…
In a recent paper it was shown that all the Hilbert space formulas for quantum probabilities can be realized as functions of geometric properties of the associated projective space, but those functions were expressed using the structures of…
Quantum groups were invented largely to provide solutions of the Yang-Baxter equation and hence solvable models in 2-dimensional statistical mechanics and one-dimensional quantum mechanics. They have been hugely successful. But not all…
How do symmetries induce natural and useful quantum structures? This question is investigated in the context of models of three interacting particles in one-dimension. Such models display a wide spectrum of possibilities for dynamical…