2134/24251 J.F. Ralph J.F. Ralph Kurt Jacobs Kurt Jacobs Mark Everitt Mark Everitt Observing quantum chaos with noisy measurements and highly mixed states Loughborough University 2017 untagged Physical Sciences not elsewhere classified 2017-03-01 09:35:07 Journal contribution https://repository.lboro.ac.uk/articles/journal_contribution/Observing_quantum_chaos_with_noisy_measurements_and_highly_mixed_states/9409964 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.