18 research outputs found
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
How to Probe for Dynamical Structure in the Collapse of Entangled States Using Nuclear Magnetic Resonance
The spin state of two magnetically inequivalent protons in contiguous atoms
of a molecule becomes entangeled by the indirect spin-spin interaction
(j-coupling). The degree of entanglement oscillates at the beat frequency
resulting from the splitting of a degeneracy. This beating is manifest in NMR
spectroscopy as an envelope of the transverse magnetization and should be
visible in the free induction decay signal. The period (approximately 1 sec) is
long enough for interference between the linear dynamics and collapse of the
wave-function induced by a Stern-Gerlach inhomogeneity to significantly alter
the shape of that envelope. Various dynamical collapse theories can be
distinguished by their observably different predictions with respect to this
alteration. Adverse effects of detuning due to the Stern-Gerlach inhomogeneity
can be reduced to an acceptable level by having a sufficiently thin sample or a
strong rf field.Comment: 6 pages, 4 figures, PDF, submitted to PR
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