Non-Markovian quantum control as coherent stochastic trajectories
Fattah Sakuldee, Simon Milz, Felix A. Pollock, Kavan Modi · Journal of Physics A Mathematical and Theoretical · 2018
Abstract We develop a notion of stochastic quantum trajectories. First, we construct a basis set of trajectories, called elementary trajectories , and go on to show that any quantum dynamical process, including those that are non-Markovian, can be expressed as a linear combination of this set. We then show that the set of processes divide into two natural classes: those that can be expressed as a convex mixture of elementary trajectories and those that cannot be. The former are shown to be entanglement breaking processes (in each step), while the latter are dubbed coherent processes . This division of processes is analogous to separable and entangled states. In the second half of the paper, we show, with an information theoretic game, that when a process is non-Markovian, coherent trajectories allow for decoupling from the environment while preserving arbitrary quantum information encoded into the system. We give explicit expressions for the temporal correlations (quantifying non-Markovianity) and show that, in general, there are more quantum correlations than classical ones. This shows that non-Markovian quantum processes are indeed fundamentally different from their classical counterparts. Furthermore, we demonstrate how coherent trajectories (with the aid of coherent control) could turn non-Markovianity into a resource. In the final section of the paper we explore this phenomenon in a geometric picture with a convenient set of basis trajectories.