Related papers: Topos Quantum Logic and Mixed States
Sorkin's coevent interpretation shifts the focus of quantum logic from the structure of a propositional lattice to the nature of truth valuations thereon. We apply this shift in emphasis to a simple formulation of the consistent histories…
We present a review on the notion of pure states and mixtures as mathematical concepts that apply for both classical and quantum physical theories, as well as for any other theory depending on statistical description. Here, states will be…
The term quantum logic has different connotations for different people, having been considered as everything from a metaphysical attack on classical reasoning to an exercise in abstract algebra. Our aim here is to give a uniform…
Non-classical probability (along with its underlying logic) is a defining feature of quantum mechanics. A formulation that incorporates them, inherently and directly, would promise a unified description of seemingly different prescriptions…
We present a conceptually new approach to describe state-of-the-art photonic quantum experiments using Graph Theory. There, the quantum states are given by the coherent superpositions of perfect matchings. The crucial observation is that…
In quantum cosmology, one applies quantum physics to the whole universe. While no unique version and no completely well-defined theory is available yet, the framework gives rise to interesting conceptual, mathematical and physical…
This paper introduces a novel type theory and logic for probabilistic reasoning. Its logic is quantitative, with fuzzy predicates. It includes normalisation and conditioning of states. This conditioning uses a key aspect that distinguishes…
The geometric form of standard quantum mechanics is compatible with the two postulates: 1) The laws of physics are invariant under the choice of experimental setup and 2) Every quantum observation or event is intrinsically statistical.…
I offer an account of how the quantum theory we have helps us explain so much. The account depends on a pragmatist interpretation of the theory: This takes a quantum state to serve solely as a source of sound advice to physically situated…
The concept of complementarity in combination with a non-Boolean calculus of propositions refers to a pivotal feature of quantum systems which has long been regarded as a key to their distinction from classical systems. But a non-Boolean…
Quantum theory has the property of "local tomography": the state of any composite system can be reconstructed from the statistics of measurements on the individual components. In this respect the holism of quantum theory is limited. We…
Construal of observable facts or events, that is, the manner in which we understand reality, is based not only on mathematical formulas of a theory suggested as a reasonable explanation for physical phenomena (like general relativity or…
This chapter provides an introduction to the use of diagrammatic language, or perhaps more accurately, diagrammatic calculus, in quantum information and quantum foundations. We illustrate the use of diagrammatic calculus in one particular…
In this paper, epistemology and ontology of quantum states are discussed based on a completely new way of founding quantum theory. The fundamental notions are conceptual variables in the mind of an observer or in the joint minds of a group…
It is shown how all the major conceptual difficulties of standard (textbook) quantum mechanics, including the two measurement problems and the (supposed) nonlocality that conflicts with special relativity, are resolved in the consistent or…
This paper presents a study of how the theory of categories leads to the creation of non classical logical systems. In particular, the case of the elementary topos of graphs, where there are three other truth values different from false and…
A survey is given summarizing the state of the art of describing information processing in Quantum Decision Theory, which has been recently advanced as a novel variant of decision making, based on the mathematical theory of separable…
In this work, I propose a way to help high school students and the general population understand quantum concepts by adopting a new inherently dual representation. Major difficulties in explaining to people the basic concepts of quantum…
One of the fundamental features of quantum mechanics is the superposition principle, a manifestation of which is embodied in quantum coherence. Coherence of a quantum state is invariably defined with respect to a preferred set of pointer…
Calculation of topological order parameters, such as the topological entropy and topological mutual information, are used to determine whether states possess topological order. Their calculation is expected to give reliable results when the…