Dartmouth Events

We show that the dynamics of any open quantum system that is initially correlated with its
environment can be described by a set of d" (or fewer) completely positive maps, where d is
the dimension of the system. Only one such map is required for the special case of no initial
correlations. The same maps describe the dynamics of any system-environment state obtained
from the initial state by a local operation on the system (and are related to the set of states to
which the environment may be steered via such local operations). The reduction of the system
dynamics to a set of completely positive maps allows known numerical and analytic tools for
uncorrelated initial states to be applied to the general case of initially-correlated states, and
provides a natural approach to quantum Markovianity for this case. Further, we show that the
set of completely positive maps can be experimentally characterized using only local
operations on the system, via a generalisation of noise spectroscopy protocols.
As an application of the above, we introduce a related Limited Access Tomography protocol,
for determining an arbitrary bipartite state via local operations on just one component. Finally,
if time permits, we will discuss our ongoing efforts towards Limited Access Total System
Characterization protocols, capable of simultaneously executing Hamiltonian Learning, State
Tomography, and Noise spectroscopy of a (bipartite) quantum system, when fast and accurate
control/measurement of only a subsystem is available.