Non-Hermitian quantum nondemolition interactions for noise-robust readout and amplification

Quantum nondemolition (QND) measurements are based on interactions between observables of a meter and a target systems that do not disturb the evolution of the target observable, enabling sensitive measurements with minimum noise. In general, QND interactions between two systems do not need to couple observables, in which case, an (non-hermitian) operator of one of the system behaves as completely decoupled for the other system, potentially evading unwanted backaction and noise effects. In this work, we present a general scheme to construct such QND interactions between a system and a target by adding a mirror system which couples to the target via the conjugate operator. We propose two applications for our general scheme: pump-depletion-free amplification and noise-robust qubit readout. In the first case, the mirror QND-scheme applied to three-wave mixing realizes quantum-limited amplification with an input-independent gain. In the second case, using a mirror QND interaction between two cavities and a qubit, we develop a dispersive readout scheme that outperforms standard readout schemes in the presence of noise, exhibiting both a faster measurement rate and a higher measurement efficiency.