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Since the pioneering works of Feynman 1) and Deutsch 2) using elements following the laws of quantum mechanics, interest has been growing in the area of so-called quantum computation. Among other things, a quantum teleportation scheme of the type proposed by Bennett et a1. 3) is of great interest from the measurement theoretical point of view. The original teleportation scheme of an unknown state iq'», which consists of the "story of Alice and Bob", however, is insufficient due to the unclear treatment of the EPR 4) problem and the assumption of von Neumann's projection postulate. At the same time, the former unclear treatment follows from the latter assumption. This teleportation scheme, based on the existence of non­ local long range correlations between EPR pairs of particles relevant to the notion of wave function collapse, necessarily leads to epistemological discussion on the nature of physical reality. Unfortunately, tentative solutions to this problem always depend on what the authors decide to define as realism. 5 ) Therefore, such philosophical arguments concerning the conceptual aspects of EPR phenomenon are beyond the realm of physics. We shall show that a quantum teleportation can be achieved within the framework of present-day quantum mechanics without resorting to von Neumann's projection postulate. Today, the naive Copenhagen interpretation is criticized for various reasons. For example, in Machida and Namiki's theory of measurement, 5),6) which does not rely upon von Neumann's projection postulate, making use of the statistical operator as the description of the quantum state and introducing the state of the apparatus system, they showed that the resolution of the difficulty concerning the wave function collapse does not consist of a demonstration of the disappearance of other branch waves, but follows from the concept of decoherence. Their theory is widely applicable, even to incomplete measurements. 5) According to these lines of thought, one of the present authors (A. M.) attempted to analyze the process of decoherence. 7) In this paper, reviewing what is a correct understanding of the EPR problem, we intend to show how we can obtain a correct teleportation scheme without resorting to von Neumann's projection postulate. A reasonable explanation of the EPR problem was given by Machida. 8) In order

A Set of Conditions for Teleportation without Resort to von Neumann's Projection Postulate