Enhanced quantum procedures that resolve difficult problems

A careful study of the classical/quantum connection with the aid of coherent states offers new insights into various technical problems. This analysis includes both canonical as well as closely related affine quantization procedures. The new tools are applied to several examples including: (1) A quantum formulation that is invariant under arbitrary classical canonical transformations of coordinates; (2) A toy model that for all positive energy solutions has singularities which are removed at the classical level when the correct quantum corrections are applied; (3) A fairly simple model field theory with non-trivial classical behavior that, when conventionally quantized, becomes trivial, but nevertheless finds a proper solution using the enhanced procedures; (4) A model of scalar field theories with non-trivial classical behavior that, when conventionally quantized, becomes trivial, but nevertheless finds a proper solution using the enhanced procedures; (5) A viable formulation of the kinematics of quantum gravity that respects the strict positivity of the spatial metric in both its classical and quantum versions; and (6) A proposal for a non-trivial quantization of [Formula: see text] that is ripe for study by Monte Carlo computational methods. All of these examples use fairly general arguments that can be understood by a broad audience.

W-like states are not necessary for totally correct quantum anonymous leader election

I show that $W$-like entangled quantum states are not a necessary quantum resource for totally correct anonymous leader election protocols. This is proven by defining a symmetric quantum state that is $n$-partite SLOCC inequivalent to the $W$ state, and then constructing a totally correct anonymous leader election protocol using this state. This result, which contradicts the previous necessity result of D'Hondt and Panangaden, furthers our understanding of how non-local quantum states can be used as a resource for distributed computation.

Quantifying the leakage of quantum protocols for classical two-party cryptography

We study quantum protocols among two distrustful parties. By adopting a rather strict definition of correctness — guaranteeing that honest players obtain their correct outcomes only — we can show that every strictly correct quantum protocol implementing a non-trivial classical primitive necessarily leaks information to a dishonest player. This extends known impossibility results to all non-trivial primitives. We provide a framework for quantifying this leakage and argue that leakage is a good measure for the privacy provided to the players by a given protocol. Our framework also covers the case where the two players are helped by a trusted third party. We show that despite the help of a trusted third party, the players cannot amplify the cryptographic power of any primitive. All our results hold even against quantum honest-but-curious adversaries who honestly follow the protocol but purify their actions and apply a different measurement at the end of the protocol. As concrete examples, we establish lower bounds on the leakage of standard universal two-party primitives such as oblivious transfer.

UNIFICATION OF SU(2)⊗U(1) USING A GENERALIZED COVARIANT DERIVATIVE AND U(3)

A generalization of the Yang–Mills covariant derivative, that uses both vector and scalar fields and transforms as a four-vector contracted with Dirac matrices, is used to simplify the Glashow–Weinberg–Salam model. Since SU(3) assigns the wrong hypercharge to the Higgs boson, it is necessary to use a special representation of U(3) to obtain all the correct quantum numbers. A surplus gauge scalar boson emerges in the process, but it uncouples from all other particles.

e+e− Annihilation in Strong Magnetic Fields

The possible existence of electron-positron plasmas in the magnetosphere of neutron stars gives rise to the question in which way the e+e− annihilation process is modified by the strong magnetic fields prevailing there. On the basis of a correct quantum mechanical treatment of the two-body problem in an external magnetic field we have calculated lifetimes of the ground state as well as of excited states of bound e+e− pairs (positronium). We find that the 1γ decay remains strictly forbidden, whereas the 2γ process is strongly enhanced with respect to the field-free case.