Abstract
Among certification techniques, those based on the violation of Bell inequalities are appealing because they do not require assumptions on the underlying Hilbert space dimension and on the accuracy of calibration methods. Such device-independent techniques have been proposed to certify the quality of entangled states, unitary operations, projective measurements following von Neumann's model and rank-one positive-operator-valued measures (POVM). Here, we show that they can be extended to the characterization of quantum instruments with post-measurement states that are not fully determined by the Kraus operators but also depend on input states. We provide concrete certification recipes that are robust to noise.
Highlights
Experiments using either NV centers [1], photon pair sources [2, 3] or neutral atoms [4] have recently been used to test Bell inequalities [5] in a very convincing way
These experiments revolutionize branches of applied physics like randomness generation [6, 7, 8, 9, 10, 11, 12] by making it device-independent, i.e. the randomness guarantees hold without assumptions on the underlying Hilbert space dimension and on the accuracy of calibration methods
We provide a recipe to certify quantum instruments that are neither projective measurements nor rank-one positive-operatorvalued measures (POVM), i.e. we certify the states conditioned on each outcome as well as the probability of each outcome
Summary
Experiments using either NV centers [1], photon pair sources [2, 3] or neutral atoms [4] have recently been used to test Bell inequalities [5] in a very convincing way. The observed Bell inequality violations have brought new and fascinating insights about nature by showing that some correlations cannot be explained by locally causal models. These experiments revolutionize branches of applied physics like randomness generation [6, 7, 8, 9, 10, 11, 12] by making it device-independent, i.e. the randomness guarantees hold without assumptions on the underlying Hilbert space dimension and on the accuracy of calibration methods. Self-testing has been applied to many entangled states [16, 17, 18, 15, 19], projective measurements [16, 20, 21, 22, 23, 24, 25, 26], and unitary operations [27]
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