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
Expectation value (quantum mechanics) A particularly simple case arises when formula_1 is a projection, and thus has only the eigenvalues 0 and 1. This physically corresponds to a "yes-no" type of experiment. In this case, the expectation value is the probability that the experiment results in "1", and it can be computed as (3) formula_24. In quantum theory, also operators with non-discrete spectrum are in use, such as the position operator formula_25 in quantum mechanics. This operator does not have eigenvalues, but has a completely continuous spectrum. In this case, the vector formula_11 can be written as a complex-valued function formula_27 on the spectrum