  In the paradigmatic example of quantum measurements, whenever one measures a
system which starts in a superposition of two states of a conserved quantity,
it jumps to one of the two states, implying different final values for the
quantity that should have been conserved. The standard law of conservation for
quantum mechanics handles this jump by stating only that the total distribution
of the conserved quantity over repeated measurements is unchanged, but states
nothing about individual cases. Here however we show that one can go beyond
this and have conservation in each individual instance. We made our arguments
in the case of angular momentum of a particle on a circle, where many
technicalities simplify, and bring arguments to show that this holds in full
generality. Hence we argue that the conservation law in quantum mechanics
should be rewritten, to go beyond its hitherto statistical formulation, to
state that the total of a conserved quantity is unchanged in every individual
measurement outcome. As a further crucial element, we show that conservation
can be localised at the level of the system of interest and its relevant frame
of reference, and is independent on any assumptions on the distribution of the
conserved quantity over the entire universe.
