Just a theorem about not completely positive maps
Tuesday, July 15, 2014
Euler lecture Hall
Imagine you are given a nonlinear stochastic Schrödinger equation which evolves in a markovian way and satisfies very general physical requirements, such as the assumption of no-faster-than-light signaling. Then the (closed) evolution of the density matrix is not, a priori, completely positive. However, in C^2, it is possible to associate a family of nonlinear stochastic Schrödinger equations to any given evolution equation of the statistical operator, whether completely positive or not . The aim is to generalise the result to Hilbert spaces of arbitrary dimension.
 Gisin, N. "Pure state quantum stochastic differential equation in C^2" - Helv. Phys. Acta; v. 63(7) p. 929-939 (1990)  Bassi, Angelo, Detlef Dürr, and Günter Hinrichs. "Uniqueness of the Equation for Quantum State Vector Collapse." Physical review letters 111.21 (2013): 210401  Diósi, Lajos. "Comment on'Uniqueness of the Equation for Quantum State Vector Collapse" arXiv:1401.6197 (2014).  Wiseman, Howard Mark, and L. Diósi. "Complete parameterization, and invariance, of diffusive quantum trajectories for Markovian open systems." Chemical Physics 268.1 (2001): 91-104.