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Entanglement maximization and dynamics via joint continuous measurement

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We investigate the quantum trajectories of jointly monitored transmon qubits, tracking measurement-induced entanglement creation as a continuous process. The quantum trajectories naturally split into low and high entanglement classes corresponding to partial parity collapse. We theoretically calculate the distribution of concurrence at any given time and show good agreement with the constructed histogram of measured concurrence trajectories. The distribution exhibits a sharp cut-off in the high concurrence limit, defining a maximal concurrence boundary. The most probable paths of the two classes, starting in a separable state and ending in either an entangled state or separable state, are found and compared with the experimentally constructed paths of the sub-ensemble. The most likely time for the transmon qubits to reach their highest concurrence can also be extracted from the most likely path analysis.