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A CNOT gate can correlate either the original control's computational label with a computational pointer, or the original target's sign-basis label with a sign-basis pointer. For the second interpretation prepare the original control in $|+⟩$ and read it in the Hadamard basis. Its two pointer states become $|+⟩$ and $|-⟩$, measuring $X$ on the original target. An apparatus role therefore depends on the ready state and readout as well as the measurement interaction.

Let $q=({\mathbf{q}}_1,\dots ,{\mathbf{q}}_N)$ denote the particle positions. In the Ghirardi--Rimini--Weber model, the wavefunction obeys the ordinary Schrödinger equationbetween random collapses. Each particle $i$ has an independent Poisson process of collapse times with rate $\lambda$. At such a time the state jumps according towhere the random centre has probability density $\Vert L_i(\mathbf{X})\psi {\Vert }^2$. The normalization is arranged so that $\int d^{3}X{L}_i(\mathbf{X}{)}^2=I$.

The original GRW scales are approximatelyAn isolated microscopic particle is therefore exceedingly unlikely to collapse during a laboratory experiment. A macroscopic pointer containing about $N\sim 10^{23}$ relevant particles has total collapse rate $N\lambda \sim 10^7{\mathrm{s}}^{-1}$ and collapse time about $10^{-7}\mathrm{s}$. After a measurement interaction correlates different microscopic outcomes with pointer positions separated by much more than $r_C$, one constituent's localization suppresses all incompatible pointer branches. This GRW amplification mechanism produces one definite macroscopic outcome with probabilities given by the Born rule, while leaving ordinary microscopic unitary time evolution almost unchanged.

For one spatial coordinate, average over the random centre of one collapse. The resulting density operator has position-space kernelIts diagonal is unchanged, so $⟨x⟩$ and $⟨x^2⟩$ are unchanged. The first derivative of the Gaussian factor vanishes at $x=x^{\prime }$, so $⟨p⟩$ is also unchanged. Its second derivative does not vanish, and the position representation of the momentum operator givesIn three dimensions the increase in total ${\mathbf{p}}^2$ is $3{\hslash }^2/(2r_C^2)$, corresponding to kinetic-energy increase $3{\hslash }^2/(4m{r}_C^2)$ per collapse. These are ensemble statements: conditioning on one specified collapse centre can shift the position moments. Repetition at rate $\lambda$ predicts GRW spontaneous heating, so precision searches for anomalous bulk heating, spontaneous radiation, momentum diffusion, and loss of matter-wave interference test the model.

An ideal measurement preserving the measured eigenspaces. In the projective setting, the selective instrument $\rho \mapsto P_j\rho P_j$ preserves every vector within outcome $j$, including coherence inside a degenerate eigenspace. Repeated measurements agree in the absence of intervening dynamics changing the measured quantity. Measuring a finer observable can destroy degeneracy coherence and need not realize the same Lüders rule instrument.

A physical measurement interaction must correlate the system with a meter; in Haroche cavity photon nondemolition experiment that meter is a chemical atom. For a measured observable $A$, a useful sufficient ideal condition is $[A,H_{\mathrm{int}}]=0$ together with $[A,H_0]=0$, where $H_{\mathrm{int}}$ is the interaction Hamiltonian operator and $H_0$ the free Hamiltonian operator. These conditions protect its eigenvalues during probing and between probes. They do not protect every other observable, nor prevent conditional quantum state changes. In particular, preserving photon number can disturb the field's quantum phase.