Entanglement and state preparation

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Abstract
When a subset of particles in an entangled state is measured, the state of the subset of unmeasured particles is determined by the outcome of the measurement. This first measurement may be thought of as a state preparation for the remaining particles. This type of measurement is important in quantum computing, quantum information theory, and in the preparation of entangled states such as the Greenberger-Horne–Zeilinger state. In this paper, we examine how the duration of the first measurement effects the state of the unmeasured subsystem. We discuss the case for which the particles are photons, but the theory is sufficiently general that it can be converted to a discussion of any type of particle. The state of the unmeasured subsytem will be a pure or mixed state depending on the nature of the measurement. In the case of quantum teleportation we show that there is an eigenvalue equation which must be satisfied for accurate teleportation. This equation provides a limitation to the states that can be accurately teleported.