The wave-particle duality of the qudit-based quantum space demonstrated by the wave-like quantum functionals

The wave-particle duality of the qudit-based quantum space is demonstrated by the wave-like quantum functionals and the particle-like quantum states. The quantum functionals are quantum objects generated by the basis qudit functionals, which are the duals of the basis qudit states. The relation between the quantum states and quantum functionals is analogous to the relation between the position and momentum in fundamental quantum physics. In particular, the quantum states and quantum functionals are related by a Fourier transform, and the quantum functionals have wave-like interpretations. The quantum functionals are not just mathematical constructs but have clear physical meanings and quantum circuit realizations. Any arbitrary qudit-based quantum state has dual characters of wave and particle, and its wave character can be evaluated by an observable and realized by a quantum circuit

Dormant entanglement that can be activated or destroyed by the basis choice of measurements on an external system

We propose a new form of entanglement called the dormant entanglement that can be activated or destroyed by the basis choice of measurements on an external system. The dormant entanglement without activation cannot be used as a quantum communication resource and has reduced correlation as compared to the Bell states. A particular form of the dormant entanglement is so weak that, without activation, no correlation in any basis can be observed between the entangled qubits. The dormant entanglement showcases a unique quantum behavior that the physical description of a local system remains incomplete until the information on all external systems entangled with the local system becomes available. For a potential application, we propose an n-party collective quantum communication channel that allows any 2 out of the n parties to activate an entanglement pair with the complete consensus of all other parties

Developable B-spline surface generation from control rulings

An intuitive design method is proposed for generating developable ruled B-spline surfaces from a sequence of straight line segments indicating the surface shape. The first and last line segments are enforced to be the head and tail ruling lines of the resulting surface while the interior lines are required to approximate rulings on the resulting surface as much as possible. This manner of developable surface design is conceptually similar to the popular way of the freeform curve and surface design in the CAD community, observing that a developable ruled surface is a single parameter family of straight lines. This new design mode of the developable surface also provides more flexibility than the widely employed way of developable surface design from two boundary curves of the surface. The problem is treated by numerical optimization methods with which a particular level of distance error is allowed. We thus provide an effective tool for creating surfaces with a high degree of developability when the input control rulings do not lie in exact developable surfaces. We consider this ability as the superiority over analytical methods in that it can deal with arbitrary design inputs and find practically useful results.Comment: 13 pages, 12 figrue