Theory of the correlated quantum Zeno effect in a monitored qubit dimer

We theoretically investigate the stochastic dynamics of two qubits subject to one- and two-site correlated continuous weak measurements. When measurements dominate over the local unitary evolution, the system's dynamics is constrained and part of the physical Hilbert space becomes inaccessible: a typical signature of the quantum Zeno (QZ) effect. In this work, we show how the competition between these two measurement processes gives rise to two distinct QZ regimes, which we dubbed and , characterized by a different topology of the allowed region of the physical Hilbert space, being a simply and nonsimply connected domain, respectively. We develop a theory based on a stochastic Gutzwiller ansatz for the wave function that is able to capture the structure of the phase diagram. Finally we show how the two QZ regimes are intimately connected to the topology of the flow of the underlying non-Hermitian Hamiltonian governing the no-click evolution.