Quantum superposition is a fundamental principle of quantum mechanics. It states that, much like waves in classical physics, any two (or more) quantum states can be added together ("superposed") and the result will be another valid quantum state; and conversely, that every quantum state can be represented as a sum of two or more other distinct states. Mathematically, it refers to a property of solutions to the Schrödinger equation; since the Schrödinger equation is linear, any linear combination of solutions will also be a solution.
An example of a physically observable manifestation of the wave nature of quantum systems is the interference peaks from an electron beam in a double-slit experiment. The pattern is very similar to the one obtained by diffraction of classical waves.
Another example is a quantum logical qubit state, as used in quantum information processing, which is a quantum superposition of the "basis states"
|
0
⟩
{\displaystyle |0\rangle }
and
|
1
⟩
{\displaystyle |1\rangle }
.
Here
|
0
⟩
{\displaystyle |0\rangle }
is the Dirac notation for the quantum state that will always give the result 0 when converted to classical logic by a measurement. Likewise
|
1
⟩
{\displaystyle |1\rangle }
is the state that will always convert to 1. Contrary to a classical bit that can only be in the state corresponding to 0 or the state corresponding to 1, a qubit may be in a superposition of both states. This means that the probabilities of measuring 0 or 1 for a qubit are in general neither 0.0 nor 1.0, and multiple measurements made on qubits in identical states will not always give the same result.