Concept
Quantum superposition
Overview
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 eigenfunctions 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
|
0
⟩
{\displaystyle |0\rangle }
and
|
1
⟩
{\displaystyle |1\rangle }
:
|
Ψ
⟩
=
c
0
|
0
⟩
+
c
1
|
1
⟩
,
{\displaystyle |\Psi \rangle =c_{0}|0\rangle +c_{1}|1\rangle ,}
where
|
Ψ
⟩
{\displaystyle |\Psi \rangle }
is the quantum state of the qubit, and
|
0
⟩
{\displaystyle |0\rangle }
,
|
1
⟩
{\displaystyle |1\rangle }
denote particular solutions to the Schrödinger equation in Dirac notation weighted by the two probability amplitudes
c
0
{\displaystyle c_{0}}
and
c
1
{\displaystyle c_{1}}
that both are complex numbers. Here
|
0
⟩
{\displaystyle |0\rangle }
corresponds to the classical 0 bit, and
|
1
⟩
{\displaystyle |1\rangle }
to the classical 1 bit. The probabilities of measuring the system in the
|
0
⟩
{\displaystyle |0\rangle }
or
|
1
⟩
{\displaystyle |1\rangle }
state are given by
|
c
0
|
2
{\displaystyle |c_{0}|^{2}}
and
|
c
1
|
2
{\displaystyle |c_{1}|^{2}}
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.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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Mere collection of numerical facts, prosecuted without regard to the ends here noted, is justly called an exercise of idle curiosity, of neither theoretical nor practical interest. 107.] Measure is the qualitative quantum, in the first place as immediate,--a quantum, to which a determinate being or a quality is attached.
Georg Wilhelm Friedrich Hegel, The Logic of Hegel
States what Quantum superposition is.
When we come to atoms, the presumption in favor of a simple law seems very slender. There is room for serious doubt whether the fundamental laws of mechanics hold good for single atoms, and it seems quite likely that they are capable of motion in more than three dimensions.
Charles S. Peirce, Chance, Love, and Logic
Close in meaning to Quantum superposition; the term itself is not named.
An important distinction, however, exists between the dynamical and the mathematical regress. The latter is engaged solely with the combination of parts into a whole, or with the division of a whole into its parts; and therefore are the conditions of its series parts of the series, and to be consequently regarded as homogeneous, and for this reason, as consisting, without exception, of phenomena. If the former…
Immanuel Kant, The Critique of Pure Reason
Close in meaning to Quantum superposition; the term itself is not named.
Philosophers who discussed Quantum superposition
Related ideas
Place in the tradition
Part of Interpretations of quantum mechanics.