Complete quantum tomography for QND detectors and generalization of QNDness.

The development of quantum non-demolition (QND) detectors for superconducting qubits, atoms or photons has been a topic of great interest in recent years. These detectors allow consecutive measurements of an observable without changing it, which has several applications in quantum computing and quantum metrology. In this work, we propose an unbiased tomographic protocol to fully characterize a QND detector, which provides us the POVM elements associated with the measurement, as well as the processes that define the state after the measurement. We test the protocol by simulating a dispersive measurement of transmon qubits, identifying the effects of several noise sources on the readout performance. Our proposal is a generalization to current characterization methods, which provides a complete quantification of the destructiveness of the detector, and hence, it can be used to improve the calibration and efficiency of state-of-the-art QND measurements. The generality of our theory allows us to improve the characterization of QND detectors for any quantum platform and under realistic experimental conditions, including photonic, atomic, and solid-state systems.