Lane P. Hughston

TL;DR: In this article, a complete constructive classification of all discrete ensembles of pure quantum states having a given density matrix is given for all positive operator valued measures with finitely many components, and it is shown that any chosen ensemble consistent with a fixed density matrix can be created at space-like separation using an entangled state depending only on ϱ.

TL;DR: In this paper, a locally invariant measure is assigned to the degree of entanglement of a given state for a general multi-particle system, and the properties of this measure are analysed for the entangled states of a pair of spin 1 2 particles.

TL;DR: In this paper, the authors use stochastic differential geometry to give a systematic geometric formulation for such models of state vector collapse and show that the probability of collapse to a given eigenstate, from any particular initial state, is, in fact, given by the usual quantum mechanical probability.

TL;DR: In this paper, the authors examined the correspondence of the two theories in detail, making a systematic use of the methods of martingale theory, and derived a set of simple formulae for the dynamics of the state in terms of a family of geometric Brownian motions, thereby constructing an explicit unravelling of the Lindblad equation.

TL;DR: In this article, a quadratic first integral of the equation of the motion for charged test particles is derived for the case of the mass of a single particle in the electromagnetic field.