Quantum nanoscience preserve and maximize coherence. Superposition is the quantum phenomena wherein an entity can simultaneously exist in two states. The classic description is the though experiment of Schroedinger’s Cat. In this gedanken experiment, the cat can be both alive and dead until the state of the cat is actually observed. Entanglement can link the quantum states of two or more objects over any distance. Entanglement lies at the heart of quantum teleportation and quantum communication. The pursuit of quantum coherence-enabled functionality includes the enabling fields of quantum nanoscientific research, such as enabling materials and tools that are directed towards the goal
Symmetry in quantum mechanics act on any four vector A = ("A", "A", "A", "A") and mix the time-like and the space-like components, according to: In relativistic quantum mechanics, wavefunctions are no longer single-component scalar fields, but now 2(2"s" + 1) component spinor fields, where "s" is the spin of the particle. The transformations of these functions in spacetime are given below. Under a proper orthochronous Lorentz transformation in Minkowski space, all one-particle quantum states locally transform under some representation of the Lorentz group: where is a finite-dimensional representation, in other words a dimensional square matrix, and is thought of as a column vector