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In contrast to classical systems, actual implementation of non-HermitianHamiltonian dynamics for quantum systems is a challenge because the processesof energy gain and dissipation are based on the underlying Hermitiansystem-environment dynamics that is trace preserving. Recently, a scheme forengineering non-Hermitian Hamiltonians as a result of repetitive measurementson an anicillary qubit has been proposed. The induced conditional dynamics ofthe main system is described by the effective non-Hermitian Hamiltonian arisngfrom the procedure. In this paper we demonstrate the effectiveness of such aprotocol by applying it to physically relevant multi-spin models, showing thatthe effective non-Hermitian Hamiltonian drives the system to a maximallyentangled stationary state. In addition, we report a new recipe to construct aphysical scenario where the quantum dynamics of a physical system representedby a given non-Hermitian Hamiltonian model may be simulated. The physicalimplications and the broad scope potential applications of such a scheme arehighlighted.

Two-qubit entanglement generation through non-Hermitian Hamiltonians induced by repeated measurements on an ancilla