Seminar 14. Von Neumann's postulate for wave function collapse: experimental verification and generalization

We review basic works on the concept of measurement in quantum mechanics from theoretical (Born 1926, von Neumann 1932, Dicke 1981, Leggett and Garg 1985) to experimental works verifying the theory (quantum Zeno effect 1990, Leggett-Garg inequalities 2024). A generalization of von Neumann's postulate to interaction-free (negative-result) measurements of single-particle states is carried out. An attempt is made to give a formulation of quantum mechanics as a physical theory, the postulates of which include: for single measurements - Born's postulate, for multiple measurements - von Neumann's postulate and its generalization for interaction-free (negative-result) measurements. From the consideration it follows quantum mechanics is non-local even for single-particle states when quantum correlations are absent.