Isoholonomic Problem and Holonomic Quantum Computation

Geometric phases accompanying adiabatic processes in quantum systems can be utilized as unitary gates for quantum computation. Optimization of control of the adiabatic process naturally leads to the isoholonomic problem. The isoholonomic problem in a homogeneous fiber bundle is formulated and solved completely.Comment: 7 pages, Proceedings of International Conference on Topology in Ordered Phases organized by Hokkaido University in March 200

Apparent Superluminal Muon-neutrino Velocity as a Manifestation of Weak Value

The result of the OPERA experiment revealed that the velocity of muon-neutrinos was larger than the speed of light. We argue that this apparent superluminal velocity can be interpreted as a weak value, which is a new concept recently studied in the context of quantum physics. The OPERA experiment setup forms a scheme that manifests the neutrino velocity as a weak value. The velocity defined in the scheme of weak measurement can exceed the speed of light. The weak velocity is not a concept associated to a single phenomenon but it is a statistical concept defined by accumulating data at separated places and by comparing the data. Neither information nor physical influence is conveyed at the weak velocity. Thus the superluminal velocity in the sense of weak value does not contradict the causality law. We propose also a model for calculating the neutrino velocity with taking neutrino oscillation into account.Comment: 5 pages, no figur

Complementarity and the nature of uncertainty relations in Einstein-Bohr recoiling slit experiment

A model of the Einstein-Bohr double-slit experiment is formulated in a fully quantum theoretical setting. In this model, the state and dynamics of a movable wall that has the double slits in it, as well as the state of a particle incoming to the double slits, are described by quantum mechanics. Using this model, we analyzed complementarity between exhibiting the interference pattern and distinguishing the particle path. Comparing the Kennard-Robertson type and the Ozawa-type uncertainty relations, we conclude that the uncertainty relation involved in the double-slit experiment is not the Ozawa-type uncertainty relation but the Kennard-type uncertainty relation of the position and the momentum of the double-slit wall. A possible experiment to test the complementarity relation is suggested. It is also argued that various phenomena which occur at the interface of a quantum system and a classical system, including distinguishability, interference, decoherence, quantum eraser, and weak value, can be understood as aspects of entanglement.Comment: 13 pages, 2 figures. The title is changed. Some references are adde

Induced Gauge Fields in the Path Integral

The path integral on a homogeneous space $G/H$ is constructed, based on the guiding principle `first lift to $G$ and then project to $G/H$'. It is then shown that this principle admits inequivalent quantizations inducing a gauge field (the canonical connection) on the homogeneous space, and thereby reproduces the result obtained earlier by algebraic approaches.Comment: 12 pages, no figures, LaTe