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arXiv:0901.0122

Gauge Boson Theory of Quantum State Reduction

Vladimir S. Mashkevich

Published Dec 31, 2008• 0 citations
arXivHTMLPDF

Abstract

A theory of quantum state reduction is advanced. It is based on two principles: (1) Gauge decomposition; (2) Maximum entropy. To wit: (1) The reduction decomposition of a state vector is the Schmidt decomposition with respect to the states of a set of (dressed) gauge boson modes; (2) The reduction instant is that of the maximum entropy of a resulting mixed state. The theory determines states undergoing the reduction, its instant, resulting pure states and their probabilities. Applications: (Polarized) photon absorption and transmission, emission, particle detection, reduction of a superposition of states, nonintegral photon states, photon and matter-photon entanglement, processes with weak bosons, and the role of gluons.

DOI
10.48550/arxiv.0901.0122

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We review two general criteria for deciding whether a pure bipartite quantum state describing a system of two identical particles is entangled or not. The first one considers the possibility of attributing a complete set of objective properties to each particle belonging to the composed system, while the second is based both on the consideration of the Slater-Schmidt number of the fermionic and bosonic analog of the Schmidt decomposition and on the evaluation of the von Neumann entropy of the one-particle reduced statistical operators. 1
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We review two general criteria for deciding whether a pure bipartite quantum state describing a system of two identical particles is entangled or not. The first one considers the possibility of attributing a complete set of objective properties to each particle belonging to the composed system, while the second is based both on the consideration of the Slater-Schmidt number of the fermionic and bosonic analogue of the Schmidt decomposition and on the evaluation of the von Neumann entropy of the one-particle reduced statistical operators.
A rigorous theory of quantum state reduction, the state change of the measured system caused by a measurement conditional upon the outcome of measurement, is developed fully within quantum mechanics without leading to the vicious circle relative to the von Neumann chain. For the basis of the theory, the local measurement theorem provides the joint probability distribution for the outcomes of local successive measurements on a noninteracting entangled system without assuming the projection postulate, and the quantum Bayes principle enables us to determine operationally the quantum state from a given information on the outcome of measurement.