Related papers: An Extension of Gleason's Theorem for Quantum Comp…
We elaborate the idea of quantum computation through measuring the correlation of a gapped ground state, while the bulk Hamiltonian is utilized to stabilize the resource. A simple computational primitive, by pulling out a single spin…
Quantum correlations often defy an explanation in terms of fundamental notions of classical physics, such as causality, locality, and realism. While the mathematical theory underpinning quantum correlations between spacelike separated…
A quantum state can be understood in a loose sense as a map that assigns a value to every observable. Formalizing this characterization of states in terms of generalized probability distributions on the set of effects, we obtain a simple…
Understanding the core content of quantum mechanics requires us to disentangle the hidden logical relationships between the postulates of this theory. Here we show that the mathematical structure of quantum measurements, the formula for…
A probabilistic propositional logic, endowed with an epistemic component for asserting (non-)compatibility of diagonizable and bounded observables, is presented and illustrated for reasoning about the random results of projective…
We prove a Gleason-type theorem for the quantum probability rule using frame functions defined on positive-operator-valued measures (POVMs), as opposed to the restricted class of orthogonal projection-valued measures used in the original…
Starting from an abstract setting for the Lueders - von Neumann quantum measurement process and its interpretation as a probability conditionalization rule in a non-Boolean event structure, the author derived a certain generalization of…
The objective of the consistent-amplitude approach to quantum theory has been to justify the mathematical formalism on the basis of three main assumptions: the first defines the subject matter, the second introduces amplitudes as the tools…
Measurement is a fundamental notion in the usual approximate quantum mechanics of measured subsystems. Probabilities are predicted for the outcomes of measurements. State vectors evolve unitarily in between measurements and by reduction of…
Classical models of computation traditionally resort to halting schemes in order to enquire about the state of a computation. In such schemes, a computational process is responsible for signalling an end of a calculation by setting a halt…
Recent developments in gravitational path integrals indicate that the nonperturbative physical Hilbert space of a closed universe is one-dimensional within each superselection sector. This raises a basic puzzle: how can a unique…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
Elaborating on our joint work with Abramsky in quant-ph/0402130 we further unravel the linear structure of Hilbert spaces into several constituents. Some prove to be very crucial for particular features of quantum theory while others…
The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…
A non-Boolean extension of the classical probability model is proposed. The non-Boolean probabilities reproduce typical quantum phenomena. The proposed model is more general and more abstract, but easier to interpret, than the quantum…
The formalism of quantum theory in Hilbert space has been applied with success to the modeling and explanation of several cognitive phenomena, whereas traditional cognitive approaches were problematical. However, this 'quantum cognition…
We propose a novel framework for the quantum geometry of expectation values over arbitrary sets of operators and establish a link between this geometry and the eigenstates of Hamiltonian families generated by these operators. We show that…
Some mathematical theories in physics justify their explanatory superiority over earlier formalisms by the clarity of their postulates. In particular, axiomatic reconstructions drive home the importance of the composition rule and the…
We generalize Lyapunov's convexity theorem for classical (scalar-valued) measures to quantum (operator-valued) measures. In particular, we show that the range of a nonatomic quantum probability measure is a weak*-closed convex set of…
Quantitative limit theorems for non-linear functionals on the Wiener space are considered. Given the possibly infinite sequence of kernels of the chaos decomposition of such a functional, an estimate for different probability distances…