Classical Robustness of Quantum Unravellings

Howard M. Wiseman, Joan A. Vaccaro

Luis Pedro García-Pintos, Adolfo del Campo, Alexey Vyacheslavovich Gorshkov +2 more

D. J Atkins, Zoe Brady, Kurt A. Jacobs +1 more

We introduce three measures which quantify the degree to which quantum systems possess the robustness exhibited by classical systems when subjected to continuous observation. Using these we show that for a fixed environmental interaction the level of robustness depends on the measurement strategy, or unravelling, and that no single strategy is maximally robust in all ways.

Howard M. Wiseman, Zoe Brady

Monitoring the fluorescent radiation of an atom unravels the master equation evolution by collapsing the atomic state into a pure state which evolves stochastically. A robust unraveling is one that gives pure states that, on average, are relatively unaffected by the master-equation evolution (which applies once the monitoring ceases). The ensemble of pure states arising from the maximally robust unraveling has been suggested to be the most natural way of representing the system [H.M. Wiseman and J.A. Vaccaro, Phys. Lett. A 250, 241 (1998)]. We find that the maximally robust unraveling of a resonantly driven atom requires an adaptive interferometric measurement proposed by Wiseman and Toombes [Phys. Rev. A 60, 2474 (1999)]. The resultant ensemble consists of just two pure states which, in the high driving limit, are close to the eigenstates of the driving Hamiltonian $\ensuremath{\Omega}{\ensuremath{\sigma}}_{x}/2.$ This ensemble is the closest thing to a classical limit for a strongly driven atom. We also find that it is possible to reasonably approximate this ensemble using just homodyne detection, an example of a continuous Markovian unraveling. This has implications for other systems, for which it may be necessary in practice to consider only continuous Markovian unravelings.

Lorenzo Fioroni, Filippo Ferrari, Emanuele Tirrito

We study the classical simulability of open quantum dynamics using random Clifford circuits doped with non-Clifford phase rotations and subject to local noise. We unravel the dynamics into stochastic quantum trajectories simulated with Clifford-augmented matrix product states, and introduce a simulation cost that quantifies the classical resources required. Optimizing this cost over stochastic unravelings, we identify noise-induced classical phases: extended parameter regions in which the dynamics can be fully disentangled by Clifford operations at arbitrary circuit depth. Their existence depends on both the noise model \emph{and} the unraveling. Using a geometric representation of quantum channels, we analytically determine optimal unravelings for a broad class of noise models, with numerical simulations confirming the predicted phase boundaries. We further relate the optimal cost to the unraveling-independent nonstabilizerness of the channel and show that, together with trajectory-resolved entanglement and nonstabilizerness, it classifies distinct dynamical regimes. Finally, we show that these classical phases disappear in the averaged density-matrix description, where no unraveling freedom remains. Our results show that the emergence of classicality in noisy random circuits depends on the measurement scheme adopted to probe it, and paves the way to further studies on the classical simulability of driven-dissipative dynamics.

Hartmut Häffner, Ferdinand Schmidt‐Kaler, W. Hänsel +8 more