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 There are rotational matrices for each spin quantum number. Evaluating the exponential for a given "z"-projection spin quantum number "s" gives a (2"s" + 1)-dimensional spin matrix. This can be used to define a spinor as a column vector of 2"s" + 1 components which transforms to a rotated coordinate system according to the spin matrix at a fixed point in space. For the simplest non-trivial case of "s" = 1/2, the spin operator is given by where the Pauli matrices in the standard representation are: The total angular momentum operator is the sum of the orbital and spin and