Quantum Stochastic Lie–Trotter Product Formula II
J. Martin Lindsay
A natural counterpart to the Lie–Trotter product formula for norm-continuous, one-parameter semigroups is proved, for the class of quasicontractive quantum stochastic (QS) operator cocycles whose expectation semigroup is norm continuous. Compared to previous such results, the assumption of a strong form of independence of the constituent cocycles is overcome. The analysis is facilitated by the development of some quantum Itô algebra. It is also shown how the maximal Gaussian component of a QS generator may be extracted—leading to a canonical decomposition of such generators, and the connection to perturbation theory is described. Finally, the quantum Itô algebra is extended to quadratic form generators, and a conjecture is formulated for the extension of the product formula to holomorphic QS cocycles.
arXiv:1707.05669•International Mathematics Research Notices•Jan 16, 2018•2 citations