later developments. Theoret. Phys. In the ﬁrst case mea-surement on a subsystem produces a pure state for another subsystem and it is good for quantum teleportation and computing. Rev. Risk Aversion In last lecture we discussed the St. Petersburg Paradox, where although the expected return from the game is infinity, only a few gamblers are willing to invest large amount of money. von Neumann’s formulation of quan-tum mechanics in terms of vectors and operators in the abstract Hilbert space provided a general framework for the interpretation of quantum theory. Von Neumann And Morgenstern Utility Function. As is well-known, these postulates differ in the case of observables with degenerate spectra. Von Neumann and Morgenstern Postulates. The use of the original von Neumann postulate eliminates this problem: instead of “action at the distance”-nonlocality, we obtain a classical measurement nonlocality. Postulates of quantum field theory. The repu-tation of von Neumann’s proof has kept on declining since this rst attack by Bell. Math. (1963) R. Alicki et al. First Postulate; Second Postulate; Third Postulate. Prog. whether the Jordan-von Neumann postulates cannot be simplified by showing that the characteristic properties of a norm (in particular, the triangle inequality) can be derived from the parallelogram identity, reinforced only by the weakest of additional assumptions. Finetti and von Neumann and Morgenstern, Savage introduced a new analytical framework ... Postulates P.1-P.4 imply the existence of a transitive and complete relation on the set of events that has the interpretation “at lease as likely to obtain as” representing the decision von Neumann’s proof echoes countless similar comments in the literature of the past ve decades, starting with John Bell’s criticism [2] that \von Neumann’s ‘very general and plausible postulates’ are absurd". Math. Most notably, von Neumann’s projection postulate is crucial when one tries to describe quantum measurement process in a physical system. von Neumann postulate induces serious problems []. Entropy of automorphisms of III von Neumann algebras. Lett. We emphasize the role of the projection postulate (determining post-measurement states) in QI and the difference between its Lüders and von Neumann versions. (1975) H. Araki Type of von Neumann algebras associated with free field. Defining quantum dynamical entropy. (1994) R. Haag Local Quantum Physics (1992) A. Connes et al. Therefore we conclude that the actual quantum measurement has as counterpart in the Clifford algebraic description, the passage from the Si to the Ni,±1 Clifford algebras, reaching in this manner the objective to reformulate von Neumann postulate on quantum measurement and proposing a self-consistent formulation of quantum theory. Acta Math. However, in the second case even starting with a pure state for a composite system, one obtains in general a statistical mixture.

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