Entanglement dynamics in a two–transmon qubit system under continuous measurement and postselection

Abstract

Abstract We investigate the role of continuous measurement and postselection in the dynamics and en
tanglement of a transmon-cavity-transmon coupled system. In the dispersive regime, characterized
by a large detuning between the transmons and the cavity, the two transmons interact via virtual
excitation of the cavity, giving rise to an effective transmon-transmon coupling. In addition to this
coherent interaction, each transmon undergoes spontaneous emission, which is continuously mon
itored through independent detection channels. By incorporating realistic detector inefficiencies,
we analyze both efficient and imperfect monitoring scenarios and demonstrate that postselection
significantly slows down the decay of entanglement compared to the unmonitored case. We formu
late the stochastic master equation for the coupled system, derive the corresponding postselected
master equation, and investigate the dynamics through the Liouvillian superoperator spectrum.
In the interaction frame, we identify the emergence of an exceptional point and characterize the
associated broken and unbroken PT-symmetric phases. We show how these phases influence the
system dynamics and the corresponding entanglement behavior. Our results provide insight into
how continuous measurement and postselection affect entanglement in dissipative quantum systems,
with potential applications in quantum information processing.