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We experimentally and theoretically investigate the quantum trajectories ofjointly monitored transmon qubits embedded in spatially separated microwavecavities. Using nearly quantum-noise limited superconducting amplifiers and anoptimized setup to reduce signal loss between cavities, we can efficientlytrack measurement-induced entanglement generation as a continuous process forsingle realizations of the experiment. The quantum trajectories of transmonqubits naturally split into low and high entanglement classes corresponding tohalf-parity collapse. The distribution of concurrence is found at any giventime and we explore the dynamics of entanglement creation in the state space.The distribution exhibits a sharp cut-off in the high concurrence limit,defining a maximal concurrence boundary. The most likely paths of the qubits'trajectories are also investigated, resulting in three probable paths,gradually projecting the system to two even subspaces and an odd subspace. Wealso investigate the most likely time for the individual trajectories to reachtheir most entangled state, and find that there are two solutions for the localmaximum, corresponding to the low and high entanglement routes. The theoreticalpredictions show excellent agreement with the experimental entangled qubittrajectory data.

Quantum trajectories and their statistics for remotely entangled quantum bits