ABSTRACT
A quantum non-demolition (QND) measurement is a specific kind of indi-
rect measurement [11]. It ideally consists of a sequence of two steps. In a
first step, the interaction between the system (S) and a probe (P ) is turned
on, in such a way that the observable of interest (called signal, AS) affects
the value of a probe observable (AP ), without being perturbed itself by
such interaction. This can be formally expressed as follows: [AS , HSP ] = 0,
[AP , HSP ] 6= 0, and ∂HSP /∂AS 6= 0, where HSP accounts for the signalprobe coupling. Such interaction results in a reversible (i.e., unitary) evolu-
tion, and generates a correlation between the states of S and P . In a second
step, AP is measured, and the outcome is used to infer the eigenstate of
AS . In order for such sequence to be repeatable, the post-measurement
evolution of AS must not become unpredictable due to: (i) possible infor-
mation that the measurement provides on its conjugated variables (AcS),
and (ii) the uncertainty that the state projection induces in AcS . The latter
condition calls for the observable to be a constant of motion of the system
Hamiltonian: ∂HS/∂A c S 6= 0 [12].
