A fundamental aspect of quantum phenomena is the non-local coherence of the quantum wave that describes the state of a particle, which is called the wave-particle duality. A consequence of this is the Heisenberg uncertainty principle according to which there is a minimum to the product of the uncertainties of the position and momentum or time and energy of the particle that is given by the Planck's constant. We plan to investigate the latter uncertainty principle in relation to the general relativistic gravitational field, using our earlier work that obtains this uncertainty relation using only measurements intrinsic to the system under investigation. We shall also use new non-local quantities that we have introduced, called modular variables, to study the non-local quantum coherence of the wave function. This will be used to investigate the Aharonov-Bohm effect (discovered by the PI), which is the non-local interaction of the wave function with the electromagnetic field. Some new aspects of scattering due to the Aharonov-Bohm effect will be studied. The latter work is relevant to a wide class of problems involving surface waves and polarized light propagating in optical fibers, where various impurities may be present.
The quantum coherence of the wave function also opens up the possibilities for secure communication using quantum systems and the construction of a quantum computer. Computations which would take a present state-of-the-art computer more than the life-time of the universe to do would be done in less than a second by a quantum computer. We shall try to use the weak measurement, discovered by the PI, to obtain better quantum communication. We shall also try to use the geometric phase discovered by the PI and a co-PI towards constructing a quantumcomputer.