= Quantum nondemolition measurement
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= Non-demolition measurement
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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>.
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