%0 Journal Article %A Ralph, J.F. %A Jacobs, Kurt %A Everitt, Mark %D 2017 %T Observing quantum chaos with noisy measurements and highly mixed states %U https://repository.lboro.ac.uk/articles/journal_contribution/Observing_quantum_chaos_with_noisy_measurements_and_highly_mixed_states/9409964 %2 https://repository.lboro.ac.uk/ndownloader/files/17027390 %K untagged %K Physical Sciences not elsewhere classified %X A fundamental requirement for the emergence of classical behavior from an underlying quantum description is that certain observed quantum systems make a transition to chaotic dynamics as their action is increased relative to ℏ. While experiments have demonstrated some aspects of this transition, the emergence of quantum trajectories with a positive Lyapunov exponent has never been observed directly. Here, we remove a major obstacle to achieving this goal by showing that, for the Duffing oscillator, the transition to a positive Lyapunov exponent can be resolved clearly from observed trajectories even with measurement efficiencies as low as 20%. We also find that the positive Lyapunov exponent is robust to highly mixed, low-purity states and to variations in the parameters of the system. %I Loughborough University