The concept of a curve traced by a state vector in the Hilbert space is introduced into the general context of quantum evolutions and its length defined. Three important curves are identified and their relation to the dynamical phase, the geometric phase and the total phase are studied. These phases are reformulated in terms of the dynamical curve, the geometric curve and the natural curve. For any arbitrary cyclic evolution of a quantum system, it is shown that the dynamical phase, the geometric phase and their sums and/or differences can be expressed as the integral of the contracted length of some suitably-defined curves. With this, the phases of the quantum mechanical wave function attain new meaning. Also, new inequalities concerning the phases are presented.

We propose a method called ‘coherence swapping’ which enables us to create superposition of a particle in two distinct paths, which is fed with initially incoherent, independent radiation. This phenomenon is also present for the charged particles, and can be used to swap the effect of flux line due to the Aharonov-Bohm effect. We propose an optical version of experimental set-up to test the coherence swapping. The phenomenon, which is simpler than entanglement swapping or teleportation, raises some fundamental questions about the true nature of wave-particle duality, and also opens up the possibility of studying the quantum erasure from a new angle.

Entangling an unknown qubit with one type of reference state is generally impossible. However, entangling an unknown qubit with two types of reference states is possible. To achieve this, we introduce a new class of states called zero sum amplitude (ZSA) multipartite, pure entangled states for qubits and study their salient features. Using shared-ZSA states, local operations and classical communication, we give a protocol for creating multipartite entangled states of an unknown quantum state with two types of reference states at remote places. This provides a way of encoding an unknown pure qubit state into a multiqubit entangled state.