Decoherence

Decoherence is the process by which quantum systems lose their ability to exhibit coherent superpositions due to interactions with their surroundings. When a system becomes entangled with many uncontrollable degrees of freedom in its environment, the relative phases between different states become inaccessible. For practical purposes, interference terms vanish, and the system evolves toward behavior that resembles a statistical mixture rather than a pure state. Decoherence occurs without any measurement and is a consequence of unitary evolution of the larger system including the environment.

In the standard framework, one writes the joint state of system S and environment E, evolves it with the total Hamiltonian, and then traces over E to obtain the reduced density matrix ρ_S. The off-diagonal elements (in a chosen basis) decay rapidly, a process called decoherence. The basis in which ρ_S becomes approximately diagonal is the pointer basis, selected by the system–environment interaction. This environment-induced superselection, or einselection, explains why certain observables appear classical.

Decoherence explains why macroscopic objects do not exhibit interference and why measurements yield definite outcomes in practice, but it does not by itself solve the measurement problem or produce a single outcome; it merely suppresses coherence in the environment and system. The effect is demonstrated in experiments such as interference of large molecules and superconducting qubits where coherence is suppressed by coupling to the environment. Decoherence rates depend on temperature, coupling strength, and the density of environmental states, and modeling requires details of both the system and its surroundings.