Semi-device-dependent blind quantum tomography

Extracting tomographic information about quantum states is a crucial task in the quest towards devising high-precision quantum devices. Current schemes typically require measurement devices for tomography that are a priori calibrated to high precision. Ironically, the accuracy of the measurement calibration is funda-mentally limited by the accuracy of state preparation, establishing a vicious cycle. Here, we prove that this cycle can be broken and the dependence on the mea-surement device's calibration significantly relaxed. We show that exploiting the natural low-rank structure of quantum states of interest suffices to arrive at a highly scalable 'blind' tomography scheme with a classically efficient post-pro cessing algorithm. We further improve the effi-ciency of our scheme by making use of the sparse structure of the calibrations. This is achieved by relaxing the blind quantum tomography problem to the de-mixing of a sparse sum of low-rank matrices. We prove that the proposed algorithm recovers a low-rank quantum state and the calibration provided that the measurement model exhibits a re-stricted isometry property. For generic measurements, we show that it requires a close-to-optimal number of measurement settings. Complementing these conceptual and mathematical insights, we numerically demonstrate that robust blind quantum tomography is possible in a practical setting inspired by an implementation of trapped ions.