Entanglement negativity as a universal non-Markovianity witness

In order to engineer an open quantum system and its evolution, it is essential to identify and control the memory effects. These are formally attributed to the non-Markovianity of dynamics that manifests itself by the evolution being indivisible in time, a property which can be witnessed by a nonmonotonic behavior of contractive functions or correlation measures. We show that by monitoring directly the entanglement behavior of a system in a tripartite setting it is possible to witness all invertible non-Markovian dynamics, as well as all (also noninvertible) qubit evolutions. This is achieved by using negativity, a computable measure of entanglement, which in the usual bipartite setting is not a universal non-Markovianity witness. We emphasize further the importance of multipartite states by showing that non-Markovianity cannot be faithfully witnessed by any contractive function of single qubits. We support our statements by an explicit example of eternally non-Markovian qubit dynamics, for which negativity can witness non-Markovianity at arbitrary timescales.

Figure 1

Negativity $E^{AB|C}$ as a function of time $t$ (in arbitrary units) for the eternally non-Markovian qubit dynamics (23) with $\alpha =2$ and $c=1/2$. The initial state ${\rho }^{ABC}$ has been set as in Eq. (16) with probabilities $p_i$ and states ${\rho }_i^{A{B}_1}$ chosen according to the constructive method of Bylicka et al. [17], leading to violation of Eq. (2) for a specific time $t^{*}>0$. The plot shows detection of non-Markovianity at $t^{*}=1$ ($t^{*}=0.01$ in the inset), which is marked on the axis and with a dashed red vertical line.