Quantum measurment is not a part of the mathematical formalism of quantum mechanics. It is an ad hoc heuristic description and method of calculation that predicts the probablilities of what will happen when an observer makes a measurement.

In standard quantum theory, an isolated system is prepared in a known state at time t. This consists of making a quantum measurement on the system and finding the experimental value for some observable quantity S(t). The future development of the system is completely described by a fully deterministic time evolution operator H(t). H(t) describes a complex probability function psi(t) for all future times. This is the "wave function" invented by Schrödinger, whose formulation of quantum mechanics is called wave mechanics.

Without any further observation, the best knowledge we have of the system state at later times depends on the (real) square of this (complex) probability amplitude function. If there are a finite number of states, we can calculate the probability of finding the system in each state.

Measurement requires the interaction of an observing instrument, assumed to be large and adequately determined. It does not require a conscious observer.

We have seen in our discussion of Schrödinger's Cat that the physical universe can be its own observer. Whenever information is encoded in information structures, we do not need the consciousness of physicists to collapse the wave function and make up the mind of the universe, as Heisenberg, Wigner, Wheeler, and others speculated.