Semi-device-independent certification of independent quantum state and measurement devices

Abstract

Certifying that quantum devices behave as intended is crucial for quantum information science. Here, methods are developed for certification of both state preparation devices and measurement devices based on prepareand-measure experiments with independent devices. The experimenter is only assumed to know the Hilbert space dimension and thus no precise characterisation of any part of the experiment is required. The certification is based on a randomised version of unambiguous state discrimination and targets the broad class of state ensembles corresponding to quantum t-designs of any size and any dimension. These quantum designs are sets of states over which the average of any t-degree polynomial equals its average over all pure states -and they accommodate many of the most useful discrete structures in quantum information processing. Furthermore, it is shown that the same experiments also certify the detection efficiency of the measurement devices, as well as their non-projective nature. The presented methods can readily be implemented in experiments.

A universal scheme for robust self-testing in the prepare-and-measure scenario

“…Finally, it is interesting to combine our method with recent findings relating state discrimination games and resource theories of measurements [41][42][43] to give analytical construction of SDI criteria for non-projective character of all extremal measurements. Note added.-See also a related work [44]. and for all x = x , a = a , y = y , and b = b , we have…”

Compounds of symmetric informationally complete measurements and their application in quantum key distribution

“…SIC-POVMs are key tools for quantum state tomography [11][12][13], which has motivated their experimental realisation in highdimensional Hilbert spaces [14][15][16]. Generally, SICs and SIC-POVMs are used in a range of protocols: quantum key distribution (QKD) [17][18][19], entanglement detection [20][21][22], device-independent random number generation [23,24], dimension witnessing [25] and characterisation of quantum de-vices [26][27][28][29][30]. Moreover, SICs have been studied in the context of quantum nonlocality [24,[31][32][33] and they have an interesting foundational role in QBism [34].…”