EPJ Quantum Technol. (2015) 2: 9
https://doi.org/10.1140/epjqt/s40507-015-0024-2

Research

A Trotter-Kato theorem for quantum Markov limits

¹ BTA VOF, Slootsekuilen 9, 5986 PE, Beringe, The Netherlands
² Dept. for Mathematics and Physics, Aberystwyth University, SY23 3BZ, Wales, United Kingdom
³ School of Electrical Engineering and Telecommunications, UNSW Australia, Sydney, NSW, 2052, Australia

^* e-mail: rog@aber.ac.uk

Received: 24 September 2014
Accepted: 14 April 2015
Published online: 30 April 2015

Abstract

Using the Trotter-Kato theorem we prove the convergence of the unitary dynamics generated by an increasingly singular Hamiltonian in the case of a single field coupling. The limit dynamics is a quantum stochastic evolution of Hudson-Parthasarathy type, and we establish in the process a graph limit convergence of the pre-limit Hamiltonian operators to the Chebotarev-Gregoratti-von Waldenfels Hamiltonian generating the quantum Itō evolution.