Related papers: Representation Systems and Quantum Structures
For general non-classical systems, we study the different classical representations that fulfill the specific context dependence imposed by the hidden measurement system formalism introduced in quant-ph/0008061. We show that the collection…
In Part I of this series we presented the general ideas of applying group-algebraic methods for describing quantum systems. The treatment was there very "ascetic" in that only the structure of a locally compact topological group was used.…
A number of recent papers treated the representation theory of partially ordered sets in unitary spaces with the so called orthoscalar relation. Such theory generalizes the classical theory which studies the representations of partially…
One of the most central and controversial element of quantum mechanics is the use of non zero vectors of a Hilbert space (or, more generally, of one dimension subspaces) for representing the state of a quantum system. In particular, the…
We introduce a definition for a 'hidden measurement system', i.e., a physical entity for which there exist: (i) 'a set of non-contextual states of the entity under study' and (ii) 'a set of states of the measurement context', and which are…
In this paper we develop an algebraic framework in which several classes of two-valued states over orthomodular lattices may be equationally characterized. The class of two-valued states and the subclass of Jauch-Piron two-valued states are…
Let us denote by $\mathcal{SOMP}$ the class of all set-representable orthomodular posets and by $\mathcal{PD SOMP}$ those elements of $\mathcal{SOMP}$ in which any pair of points in the underlying set $P$ can be distinguished by a set…
We offer a systematic account of decomposition of quantum systems into parts. Different decompositions (structures) are mutually linked via the proper linear canonical transformations. Different kinds of structures, as well as their…
In classical physics, a single measurement can in principle reveal the state of a system. However, quantum theory permits numerous non-equivalent measurements on a physical system, each providing only limited information about the state.…
In this work we study the convex set of quantum states from a quantum logical point of view. We consider an algebraic structure based on the convex subsets of this set. The relationship of this algebraic structure with the lattice of…
To make progress in science, we often build abstract representations of physical systems that meaningfully encode information about the systems. The representations learnt by most current machine learning techniques reflect statistical…
Quantum information and computation may serve as a source of useful axioms and ideas for the quantum logic/quantum structures project of characterizing and classifying types of physical theories, including quantum mechanics and classical…
We study modular ortholattices in the variety generated by the finite dimensional ones from an equational and geometric point of view. We relate this to coordinatization results.
There is a unique finite group that lies inside the 2-dimensional unitary group but not in the special unitary group, and maps by the symmetric square to an irreducible subgroup of the 3-dimensional real special orthogonal group. In an…
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…
We suggest that a certain one-to-one parametrization of completely positive maps on the matrix algebra might be useful in the study of quantum channels. This is illustrated in the case of binary quantum channels. While the algorithm is…
A new realist interpretation of quantum mechanics is introduced. Quantum systems are shown to have two kinds of properties: the usual ones described by values of quantum observables, which are called extrinsic, and those that can be…
Quantum logical axiomatic systems for quantum theory usually include a postulate that a lattice under consideration is orthomodular. We propose a derivation of orthomodularity from an information-theoretic axiom. This provides conceptual…
In complete analogy with the classical situation (which is briefly reviewed) it is possible to define bi-Hamiltonian descriptions for Quantum systems. We also analyze compatible Hermitian structures in full analogy with compatible Poisson…
For the standard lattice model of information structures, we derive a reduced poset representation which provides the same informational content as the complete lattice structure which derives it. Rational agents can recover the complete…