  This note is devoted to some foundational aspects of quantum mechanics (QM)
related to quantum information (QI) theory, especially quantum teleportation
and ``one way quantum computing.'' We emphasize the role of the projection
postulate (determining post-measurement states) in QI and the difference
between its L\"uders and von Neumann versions. These projection postulates
differ crucially in the case of observables with degenerate spectra. Such
observables play the fundamental role in operations with entangled states: any
measurement on one subsystem is represented by an observable with degenerate
spectrum in the Hilbert space of a composite system. If von Neumann was right
and L\"uders was wrong the canonical schemes of quantum teleportation and ``one
way quantum computing'' would not work. Surprisingly, we found that, in fact,
von Neumann's description of measurements via refinement implies (under natural
assumptions) L\"uders projection postulate. It seems that this important
observation was missed during last 70 years. This result closed the problem of
the proper use of the projection postulate in quantum information theory. One
can proceed with L\"uders postulate (as people in quantum information really
do).
