Chaos in Continuously-Monitored Qubits: An Extremal-Probability Path Approach

We apply an optimal path approach to the stochastic dynamics of qubits subject to continuous measurement and a time-dependent Hamiltonian. Optimal paths, defined as extremal-probability paths between initial and final boundary conditions, can exhibit chaotic behavior. Examples will be given of driven qubit systems whose optimal paths exhibit a positive Lyapunov exponent. These examples will be used to illustrate how optimal-path chaos is related to the statistics and underlying stochastic quantum trajectories obtained from continuous measurement. We will discuss how these chaotic dynamics impact the long-term predictability of continuously monitored systems.