Nonunital non-Markovianity of quantum dynamics

Trace distance is available to capture the dynamical information of the unital aspect of a quantum process. However, it cannot reflect the nonunital part. So the nondivisibility originating from the nonunital aspect cannot be revealed by the corresponding measure based on the trace distance. We provide a measure of nonunital non-Markovianity of quantum processes, which is a supplement to Breuer-Laine-Piilo (BLP) non-Markovianity measure. A measure of the degree of the nonunitality is also provided.

Figure 1

Sketch of the information flow picture for non-Markovianity [4]. According to this scenario, the loss of distinguishability of the system's states indicates the information flow from the system to the reservoir. If the dynamics is Markovian, the information flow is always outward, represented by the thick green arrow. Non-Markovian behaviors occurs when there is inward information flow, represented by the thin orange arrow, bringing some distinguishability back to the system.

Figure 2

(a) Evolution of trace distance and the Bures distance between two evolving states of a two-level system under the variant generalized amplitude damping channel, initially from the maximal mixed state ${\varrho }_0=\mathbb{1}/2$ and its trajectory state ${\varrho }_{\tau }={\mathcal{E}}_{\tau }\left({\varrho }_0\right)$. (b) The evolution of $g\left(t\right)$ defined by Eq. (21), whose integral with respect to time $t$ is the RHP measure for non-Markovianity. In these plots, the parameters are taken as $\tau =10$ and $\omega =5$.