2013/06/06 by Tristan Benoist, Clément Pellegrini, Clement Pellegrini
Computer Science · Mathematics · Physics and Astronomy · #Girsanov theorem #Master equation #Open quantum system #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum algorithm #Quantum operation #Quantum probability #Quantum process #Stochastic differential equation #math-ph #math.MP #math.PR #quant-ph
paper · pdf · doi:10.1007/s00220-014-2029-6
published as Commun. Math. Phys. 331, 703-723 (2014)
arxiv created 2013/06/06 · openalex publication_date 2014/04/21 · arxiv updated 2015/03/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A quantum system S undergoing continuous time measurement is usually described by a jump-diffusion stochastic differential equation. Such an equation is called a stochastic master equation and its solution is called a quantum trajectory. This solution describes actually the evolution of the state of S. In the context of Quantum Non Demolition measurement, we investigate the large time behavior of this solution. It is rigorously shown that, for large time, this solution behaves as if a direct Von Neumann measurement has been performed at time 0. In particular the solution converges to a random pure state which is related to the wave packet reduction postulate. Using theory of Girsanov transformation, we determine precisely the exponential rate of convergence towards this random state. The important problem of state estimation (used in experiment) is also investigated.