Quantum collapse as reduction from a continuum of conditional amplitudes in an entangled state to a single actualized amplitude in the collapsed state

Abstract

According to the Copenhagen interpretation of quantum mechanics a measurement leads to the collapse of a quantum system. A unified description of a quantum system before and after measurement of the position r1a and the spin s1a of one of its electrons is proposed based on the conditional amplitude and its density. Quantum collapse is described as reduction from continuum of the conditional amplitudes {φ(x2,⋯,xN|r1h,s1h)} in an initial quantum state to the single actualized amplitude φ(x2, ⋯,xN|r1a,s1a) in a collapsed state. The latter state contains the information about quantum entanglement, the extraction of which with fragment entanglement measure is demonstrated for the realistic valence bond models of the dissociating dihydrogen and ethylene molecules.