Quantum Surveying: How Entangled Pairs Act as Measuring Rods on Manifolds of Generalized Coherent States

Generalized coherent states arise from reference states by the action of locally compact transformation groups and thereby form manifolds on which there is an invariant measure. It is shown that this implies the existence of canonically associated Bell states that serve as measuring rods by relating the metric geometry of the manifold to the observed EPR correlations. It is further shown that these correlations can be accounted for by a hidden variable theory which is non-local but invariant under the stability group of the reference state.Comment: 14 pages, 0 figures, plain te

Conservation of Statistics and Generalized Grassmann Numbers

Conservation of statistics requires that fermions be coupled to Grassmann external sources. Correspondingly, conservation of statistics requires that parabosons, parafermions and quons be coupled to external sources that are the appropriate generalizations of Grassmann numbers.Comment: 10 pages, late

Derivation of the Rules of Quantum Mechanics from Information-Theoretic Axioms

Conventional quantum mechanics with a complex Hilbert space and the Born Rule is derived from five axioms describing properties of probability distributions for the outcome of measurements. Axioms I,II,III are common to quantum mechanics and hidden variable theories. Axiom IV recognizes a phenomenon, first noted by Turing and von Neumann, in which the increase in entropy resulting from a measurement is reduced by a suitable intermediate measurement. This is shown to be impossible for local hidden variable theories. Axiom IV, together with the first three, almost suffice to deduce the conventional rules but allow some exotic, alternatives such as real or quaternionic quantum mechanics. Axiom V recognizes a property of the distribution of outcomes of random measurements on qubits which holds only in the complex Hilbert space model. It is then shown that the five axioms also imply the conventional rules for all dimensions.Comment: 20 pages, 6 figure