Editing Quantum superposition (section)

{{Short description|Principle of quantum mechanics}}
{{broader|Superposition principle}}
{{Use dmy dates|date=April 2020}}
[[File:Quantum superposition of states and decoherence.ogv|thumb|upright=1.5|Quantum superposition of states and decoherence]]
{{Quantum mechanics|cTopic=Fundamental concepts}}

'''Quantum superposition''' is a fundamental principle of [[quantum mechanics]] that states that linear combinations of solutions to the [[Schrödinger equation]] are also solutions of the Schrödinger equation. This follows from the fact that the Schrödinger equation is a [[linear differential equation]] in time and position. More precisely, the state of a system is given by a [[linear combination]] of all the [[eigenfunction]]s of the Schrödinger equation governing that system.

An example is a [[qubit]] used in [[quantum information processing]]. A qubit state is most generally a superposition of the basis states <math>|0 \rangle</math> and <math>|1 \rangle</math>:

: <math>|\Psi \rangle = c_0|0\rangle + c_1|1\rangle,</math>

where <math>|\Psi \rangle</math> is the [[quantum state]] of the qubit, and <math>|0 \rangle</math>, <math>|1 \rangle</math> denote particular solutions to the Schrödinger equation in [[Bra–ket notation|Dirac notation]] weighted by the two [[probability amplitude]]s <math>c_0</math> and <math>c_1</math> that both are complex numbers. Here <math>|0 \rangle </math> corresponds to the classical 0 [[bit]], and <math>|1 \rangle </math> to the classical 1 bit. The probabilities of measuring the system in the <math>|0 \rangle</math> or <math>|1 \rangle</math> state are given by <math>|c_0|^2</math> and <math>|c_1|^2</math> respectively (see the [[Born rule]]). Before the measurement occurs the qubit is in a superposition of both states.

The interference fringes in the [[double-slit experiment]] provide another example of the superposition principle.