Decoherence

Decoherence is the dynamical suppression of locally observable interference caused by entanglement with uncontrolled degrees of freedom. It explains why some reduced states become approximately diagonal in a stable basis, but it is not the same thing as wavefunction collapse.

Formula Hook

For a system $S$ and environment $E$, the locally accessible state is the reduced density operator

$$\rho_S = \operatorname{Tr}_E \lvert\Psi\rangle\langle\Psi\rvert.$$

If

$$\lvert\Psi\rangle = \sum_i c_i\lvert i\rangle\lvert E_i\rangle,$$

then the reduced-state matrix elements in the $\{\lvert i\rangle\}$ basis contain environmental overlaps:

$$(\rho_S)_{ij} = c_i c_j^* \langle E_j\rvert E_i\rangle.$$

When $\langle E_j\rvert E_i\rangle\approx0$ for $i\ne j$, off-diagonal interference terms are suppressed for measurements on $S$ alone.

Canonical Home

See Decoherence Preview for the Core-level bridge, Reduced Density Matrices for the partial-trace construction, and What Measurement Formalism Does Not Settle for interpretive boundaries.

Common Confusions

• Decoherence suppresses interference in a reduced state; it does not by itself select a unique realized outcome.
• The global system-plus-environment state may remain pure even when the subsystem state looks mixed.
• The preferred or pointer basis is dynamical and model-dependent.
• Decoherence timescales depend on the coupling, environment, coarse-graining, and measured observables.

Related Entries

• Density Matrix
• Entanglement
• Superposition

References

• E. Joos et al., Decoherence and the Appearance of a Classical World in Quantum Theory, 2nd ed., Springer, 2003.
• M. Schlosshauer, Decoherence and the Quantum-to-Classical Transition, Springer, 2007.
• W. H. Zurek, “Decoherence, einselection, and the quantum origins of the classical,” Reviews of Modern Physics 75, 715-775, 2003.