Characterizing Quantum Instruments: From Nondemolition Measurements to Quantum Error Correction

In quantum information processing operations are often processed alongside measurements which result in classical data. Due to the gain of measurement outputs non-unitary dynamical processes can take place on system, for common channel descriptions fail describe time evolution. Quantum correctly treated by means so-called instruments capturing both and post-measurement states. Here we present a general recipe characterize its experimental implementation analysis. Thereby, full dynamics instrument be captured, exhibiting details that would overlooked with tomography techniques. For illustration, apply our characterization technique used detection qubit loss leakage, was recently implemented as building block error correction (QEC) experiment (Nature 585, 207-210 (2020)). Our analysis reveals unexpected in-depth about failure modes instrument. We then numerically study implications these QEC performance, when is employed protocols logical qubit. results highlight importance careful modelling instruments, compared simplistic hardware-agnostic phenomenological noise models, predict undesired behavior faulty instruments. The presented methods directly applicable generic