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Quantum decoherence arises when different system alternatives correlate with distinguishable environmental states. For an initially uncorrelated state, a measurement-like unitary time evolution can produceTaking the environmental partial trace givesThe environmental overlap suppresses locally observable quantum coherence. Scattered photons, surrounding gas and uncontrolled apparatus variables can carry away such records. The interaction often singles out robust states forming a pointer basis. Decoherence can be much faster than thermal energy relaxation because recording a macroscopic distinction need not transfer much energy.

The overall state can remain pure and evolve unitarily even when the system alone looks like a classical mixture. Discarding environmental information is therefore not, by itself, a proof of fundamental wavefunction collapse or a solution to the definite-outcome measurement problem. A small controlled environment can return coherence, as in the single-qubit environment dephasing model; practical irreversibility arises when recovering the many dispersed records becomes inaccessible. In an interferometer, varying gas pressure or an independently controllable path marker tests the dependence of fringe contrast on this environmental coupling. Quantum computation must suppress or correct such unwanted system–environment entanglement to preserve the intended interference.

Write $H=g{I}_S\otimes Z_D\otimes X_E$, with $Z_D={\Lambda }_{\uparrow }-{\Lambda }_{\downarrow }$. The orthogonal projection operators obey ${\Lambda }_{\uparrow }{\Lambda }_{\downarrow }=0$ and ${\Lambda }_j^2={\Lambda }_j$. Hence $[Z_D,{\Lambda }_j]=0$, and the remaining tensor factors commute with detector operators. ThereforeThe environment interaction preserves these detector populations, making their basis a candidate pointer basis. It can change their relative coherence without flipping the stored labels.

The absence of visibly strange superposed records is an observational constraint, but it does not by itself uniquely confirm a physical collapse law. A macroscopic superposition in the global state need not mean that an observer sees two contradictory records simultaneously. Decoherence can suppress interference between record branches, and interpretations with additional configurations or branch-relative observers can reproduce definite experiences without stochastic collapse of the universal wavefunction.

Conversely, simply invoking decoherence does not prove that one global outcome has been selected. A reduced density matrix diagonal in a pointer basis gives the same local statistics as a classical mixture but can arise from an entangled pure state. That distinction is central to the measurement problem. The adequacy of a no-collapse account requires its own explanation of observers, records and their probabilities, rather than the assertion that small off-diagonal terms settle everything.

To distinguish dynamical collapse empirically one seeks consequences beyond the common prediction of stable records, such as a specified loss of interference with mass or separation, anomalous heating or spontaneous radiation. Those predictions depend on collapse parameters and how the law couples to matter. Experiments can constrain those models while ordinary everyday definiteness alone underdetermines the alternative laws.

Thus familiar outcomes are evidence that any acceptable theory must explain. They support collapse over a naive theory that literally predicts an experienced unresolved superposition without a record account, but not over every developed no-collapse interpretation with the same outcome statistics. A fair comparison tests the full alternatives and their likelihoods, rather than treating interpretive disagreement as an observation of collapse itself.^[ref]

Published in Physical Review D 24, starting at page 1516, on 15 September 1981. The apparatus-environment interaction is used to identify robust recorded observables and their pointer basis.

Quantum decoherence is the suppression of observable quantum phase relations through interaction with unobserved degrees of freedom. A simple model starts with $(a|0⟩+b|1⟩)|E⟩$ and correlates the alternatives with environmental states:Taking the partial trace multiplies the off-diagonal entry of the reduced density matrix by $⟨E_1|E_0⟩$. If the environmental records become nearly orthogonal, interference between the two alternatives becomes locally inaccessible even though the joint state can remain pure.

Preserving diagonal populations is a property of dephasing, not a general requirement for quantum decoherence. An amplitude damping channel, for example, changes an excited-state population as ${\rho }_{11}\mapsto (1-p){\rho }_{11}$ while suppressing coherence as ${\rho }_{01}\mapsto \sqrt{1-p}{\rho }_{01}$. Thus energy relaxation and quantum decoherence can occur together, with different rates. Pure dephasing instead preserves populations in its selected pointer basis.^[ref]