Related papers: Coevents as Beables
We propose a quantum clock synchronization protocol in which Bob makes a remote measurement on Alice's quantum clock via a third qubit acting as its proxy. It is shown that the resulting correlations are dependent on the choice of the…
This paper is the second in a series whose goal is to develop a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of…
In this paper, we construct a sheaf-based topos quantum theory. It is well known that a topos quantum theory can be constructed on the topos of presheaves on the category of commutative von Neumann algebras of bounded operators on a Hilbert…
In a recent paper Kent has pointed out that in consistent histories quantum theory it is possible, given initial and final states, to construct two different consistent families of histories, in each of which there is a proposition that can…
Tableaux originate as a decision method for a logical language. They can also be extended to obtain a structure that spells out all the information in a set of sentences in terms of truth value assignments to atomic formulas that appear in…
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…
In this paper, we introduce a new definition of sheaves on semicartesian quantales, providing first examples and categorical properties. We note that our sheaves are similar to the standard definition of a sheaf on a locale, however, we…
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…
The collection of all topologies on the set of three points is studied treating the topology as quantum-like observable. It turns out to be possible under the assumption of the asymmetry between the spaces of bra- and ket-vectors. The…
Previous derivations of the sum and product rules of probability theory relied on the algebraic properties of Boolean logic. Here they are derived within a more general framework based on lattice theory. The result is a new foundation of…
We provide a cohomological framework for contextuality of quantum mechanics that is suited to describing contextuality as a resource in measurement-based quantum computation. This framework applies to the parity proofs first discussed by…
We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One…
The questions we raise in this letter are as follows: What is the most general representation of a quantum state at a single point in time? Can we adapt the current formalisms to situations where the order of quantum operations is…
The causal structure of space-time offers a natural notion of an opposite or orthogonal in the logical sense, where the opposite of a set is formed by all points non time-like related with it. We show that for a general space-time the…
We develop a new interpretation of quantum theory by combining insights from extended Wigner's friend scenarios and quantum causal modelling. In this interpretation, which synthesizes ideas from relational quantum mechanics and consistent…
It is shown how, given a "probability data table" for a quantum or classical system, the representation of states and measurement outcomes as vectors in a real vector space follows in a natural way. Some properties of the resulting sets of…
We propose various methods for combining or amalgamating propositional languages and deductive systems. We make heavy use of quantales and quantale modules in the wake of previous works by the present and other authors. We also describe…
We consider some generalization of the theory of quantum states and demonstrate that the consideration of quantum states as sheaves can provide, in principle, more deep understanding of some well-known phenomena. The key ingredients of the…
We analyse a proposition which considers quantum theory as a mere tool for calculating probabilities for sequences of outcomes of observations made by an Observer, who him/herself remains outside the scope of the theory. Predictions are…
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…