Jump-time unraveling of Markovian open quantum systems

We introduce jumptime unraveling as a distinct description of open quantum systems. As our starting point, we consider jump trajectories, which emerge, physically, from continuous measurements, or, formally, the Markovian master equations. If stochastically evolving trajectories are ensemble-averaged at specific times, resulting states solutions to associated equation. demonstrate that can also be counts. The jumptime-averaged then discrete, deterministic evolution equation, with time replaced by count. This represents trace-preserving dynamical map if and only system does not exhibit dark states. In presence states, on other hand, may decay into eventually terminate. Jumptime-averaged operationally accessible in measurement schemes, when jumps detected used trigger readout measurements. illustrate examples two-level undergoing relaxation or dephasing, damped harmonic oscillator, free particle exposed collisional decoherence.