Compression Bases in Unital Groups

We study unital groups with a distinguished family of compressions called a compression base. A motivating example is the partially ordered additive group of a von Neumann algebra with all Naimark compressions as the compression base.Comment: 8 page

Topological Test Spaces

A test space is the set of outcome-sets associated with a collection of experiments. This notion provides a simple mathematical framework for the study of probabilistic theories -- notably, quantum mechanics -- in which one is faced with incommensurable random quantities. In the case of quantum mechanics, the relevant test space, the set of orthonormal bases of a Hilbert space, carries significant topological structure. This paper inaugurates a general study of topological test spaces. Among other things, we show that any topological test space with a compact space of outcomes is of finite rank. We also generalize results of Meyer and Clifton-Kent by showing that, under very weak assumptions, any second-countable topological test space contains a dense semi-classical test space.Comment: 12 pp., LaTeX 2e. To appear in Int. J. Theor. Phy

A generalized no-broadcasting theorem

We prove a generalized version of the no-broadcasting theorem, applicable to essentially \emph{any} nonclassical finite-dimensional probabilistic model satisfying a no-signaling criterion, including ones with ``super-quantum'' correlations. A strengthened version of the quantum no-broadcasting theorem follows, and its proof is significantly simpler than existing proofs of the no-broadcasting theorem.Comment: 4 page

Local Quantum Measurement and No-Signaling Imply Quantum Correlations

We show that, assuming that quantum mechanics holds locally, the finite speed of information is the principle that limits all possible correlations between distant parties to be quantum mechanical as well. Local quantum mechanics means that a Hilbert space is assigned to each party, and then all local positive-operator-valued measurements are (in principle) available; however, the joint system is not necessarily described by a Hilbert space. In particular, we do not assume the tensor product formalism between the joint systems. Our result shows that if any experiment would give nonlocal correlations beyond quantum mechanics, quantum theory would be invalidated even locally.Comment: Published version. 5 pages, 1 figure

Quantum Structures: An Attempt to Explain the Origin of their Appearance in Nature

We explain the quantum structure as due to the presence of two effects, (a) a real change of state of the entity under influence of the measurement and, (b) a lack of knowledge about a deeper deterministic reality of the measurement process. We present a quantum machine, where we can illustrate in a simple way how the quantum structure arises as a consequence of the two mentioned effects. We introduce a parameter epsilon that measures the size of the lack of knowledge on the measurement process, and by varying this parameter, we describe a continuous evolution from a quantum structure (maximal lack of knowledge) to a classical structure (zero lack of knowledge). We show that for intermediate values of epsilon we find a new type of structure, that is neither quantum nor classical. We apply the model that we have introduced to situations of lack of knowledge about the measurement process appearing in other regions of reality. More specifically we investigate the quantum-like structures that appear in the situation of psychological decision processes, where the subject is influenced during the testing, and forms some of his opinions during the testing process. Our conclusion is that in the light of this explanation, the quantum probabilities are epistemic and not ontological, which means that quantum mechanics is compatible with a determinism of the whole.Comment: 22 pages, 8 figure

Unified Framework for Correlations in Terms of Local Quantum Observables

We provide a unified framework for nonsignalling quantum and classical multipartite correlations, allowing all to be written as the trace of some local (quantum) measurements multiplied by an operator. The properties of this operator define the corresponding set of correlations.We then show that if the theory is such that all local quantum measurements are possible, one obtains the correlations corresponding to the extension of Gleason's Theorem to multipartite systems. Such correlations coincide with the quantum ones for one and two parties, but we prove the existence of a gap for three or more parties.Comment: 4 pages, final versio

An Intrisic Topology for Orthomodular Lattices

We present a general way to define a topology on orthomodular lattices. We show that in the case of a Hilbert lattice, this topology is equivalent to that induced by the metrics of the corresponding Hilbert space. Moreover, we show that in the case of a boolean algebra, the obtained topology is the discrete one. Thus, our construction provides a general tool for studying orthomodular lattices but also a way to distinguish classical and quantum logics.Comment: Under submission to the International Journal of Theoretical Physic