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{{Quantum book backlink|Open quantum systems}}
'''Quantum decoherence''' is the process by which a quantum system loses its ability to exhibit coherent superposition due to interaction with its environment. It explains how classical behavior emerges from quantum systems without invoking wavefunction collapse.<ref name="Zurek2003">{{cite book
|last=Zurek
|first=Wojciech H.
|title=Decoherence and the Transition from Quantum to Classical
|publisher=Springer
|year=2003
|url=https://link.springer.com/chapter/10.1007/978-3-540-35775-9_1
}}</ref><ref name="MIT_OCW">{{cite web |url=https://ocw.mit.edu/courses/22-51-quantum-theory-of-radiation-interactions-fall-2012/resources/mit22_51f12_ch8/ |title=22.51 Course Notes, Chapter 8: Open Quantum Systems |website=MIT OpenCourseWare |access-date=2026-04-12}}</ref>
Decoherence plays a central role in quantum measurement, quantum information, and the quantum-to-classical transition.

[[File:Quantum_decoherence.svg|thumb|400px|Decoherence describes the loss of quantum coherence due to interaction with the environment, leading to the emergence of classical behavior.]]

=Quantum Decoherence=
== Basic mechanism ==

In quantum mechanics, a system may exist in a superposition of states:

<math>
|\psi\rangle = \alpha |0\rangle + \beta |1\rangle.
</math>

The corresponding density matrix is

<math>
\rho =
\begin{pmatrix}
|\alpha|^2 & \alpha \beta^* \\
\alpha^* \beta & |\beta|^2
\end{pmatrix}.
</math>

The off-diagonal elements represent quantum coherence.

=== Interaction with environment ===

When the system interacts with an environment, it becomes entangled with environmental degrees of freedom:

<math>
|\psi\rangle \otimes |E_0\rangle
\rightarrow
\alpha |0\rangle \otimes |E_0'\rangle
+
\beta |1\rangle \otimes |E_1'\rangle.
</math>

Tracing out the environment yields a reduced density matrix:

<math>
\rho \rightarrow
\begin{pmatrix}
|\alpha|^2 & \alpha \beta^* \langle E_1'|E_0'\rangle \\
\alpha^* \beta \langle E_0'|E_1'\rangle & |\beta|^2
\end{pmatrix}.
</math>

If the environment states become orthogonal, the coherence terms vanish.

=== Loss of coherence ===

In the limit

<math>
\langle E_0'|E_1'\rangle \rightarrow 0,
</math>

the density matrix becomes diagonal:

<math>
\rho \rightarrow
\begin{pmatrix}
|\alpha|^2 & 0 \\
0 & |\beta|^2
\end{pmatrix}.
</math>

This corresponds to a classical statistical mixture.<ref name="Zurek2003" />

== Decoherence in master equations ==

Decoherence is naturally described within the framework of quantum master equations.

=== Lindblad description ===

In the Lindblad equation, decoherence arises from dissipative terms:

<math>
\frac{d\rho}{dt}
=
-\frac{i}{\hbar}[\hat{H},\rho]
+
\sum_k
\left(
L_k \rho L_k^\dagger
-\frac{1}{2}\{L_k^\dagger L_k,\rho\}
\right).
</math>

Certain Lindblad operators suppress off-diagonal elements of <math>\rho</math>.

=== Pure dephasing ===

A simple model of decoherence is pure dephasing:

<math>
L = \sqrt{\gamma_\phi}\,\sigma_z.
</math>

This leaves populations unchanged but causes exponential decay of coherence:

<math>
\rho_{01}(t) = \rho_{01}(0) e^{-\gamma_\phi t}.
</math>

== Pointer states ==

Decoherence does not affect all states equally. Certain states remain stable under environmental interaction.

=== Definition ===

'''Pointer states''' are the states that remain robust under decoherence. They are selected by the system–environment interaction.<ref name="Zurek2003" />

=== Environment-induced superselection ===

The process by which pointer states emerge is called '''einselection''' (environment-induced superselection).

These states form a preferred basis in which the density matrix becomes diagonal.

== Decoherence timescales ==

Decoherence typically occurs extremely rapidly compared to other dynamical processes.

=== Decoherence time ===

The decoherence time <math>\tau_D</math> characterizes the decay of coherence:

<math>
\rho_{ij}(t) \sim e^{-t/\tau_D}.
</math>

For macroscopic systems, <math>\tau_D</math> is often extremely short.

=== Comparison with relaxation ===

* decoherence time: loss of phase coherence
* relaxation time: energy dissipation

Usually:

<math>
\tau_D \ll \tau_R.
</math>

This explains why classical behavior appears so quickly.

== Role in measurement ==

Decoherence provides a mechanism for the apparent collapse of the wavefunction.

=== Measurement interaction ===

During measurement, the system becomes entangled with a measuring device and environment.

Decoherence suppresses interference between different outcomes, making them effectively classical.

=== Classical outcomes ===

After decoherence, the system behaves as if it were in one of several classical states with certain probabilities.

However, decoherence alone does not select a single outcome; it explains the absence of interference.<ref name="MIT_OCW" />

== Applications ==

Decoherence is central to many areas of modern physics.

=== Quantum information ===

It is the main obstacle to building stable quantum computers, as it destroys qubit coherence.<ref name="QubitReview">{{cite journal |last=Kjaergaard |first=Morten |last2=Schwartz |first2=Michael E. |last3=Braumüller |first3=Jochen |last4=Krantz |first4=Philip |last5=Wang |first5=J. I.-J. |last6=Gustavsson |first6=Simon |last7=Oliver |first7=William D. |title=Engineering high-coherence superconducting qubits |journal=Nature Reviews Materials |volume=5 |pages=309–324 |year=2020 |url=https://www.nature.com/articles/s41578-021-00370-4 |doi=10.1038/s41578-021-00370-4}}</ref>

=== Quantum optics ===

It explains line broadening, photon loss, and coherence decay in optical systems.

=== Foundations of quantum mechanics ===

Decoherence provides a physical explanation for the emergence of classical reality from quantum theory.

== Physical significance ==

Quantum decoherence bridges the gap between microscopic quantum laws and macroscopic classical phenomena. It explains why interference effects are not observed in everyday systems and provides a consistent framework for understanding open quantum systems.<ref name="Zurek2003" />

It is one of the key concepts in modern quantum theory.

=See also=
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also}}

=References=
{{reflist|3}}

{{Author|Harold Foppele}}

{{Sourceattribution|Quantum Decoherence|1}}

Physics:Quantum Decoherence - Revision history

imported>WikiHarold: Repair Quantum Collection B backlink template

imported>WikiHarold: Repair Quantum Collection B backlink template