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Concept of random measurements: a quantum state is distributed and is assumed to undergo (unknown) local unitary transformations.
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Quantum entanglement is one of the core features of quantum theory. While it is typically revealed by measurements along carefully chosen directions, here we review different methods based on so-called random or randomized measurements. Although this approach might seem inefficient at first, sampling correlations in various random directions is a p...
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... for detection and classification of entanglement in this scenario. Finally, we will discuss their approach for selecting local measurement directions based on spherical t-designs. To illustrate the scenario, we can first think of a twoqubit state whose subsystems are sent to two observers via unitary but unknown quantum channels as shown in Fig. 1. Hence, the goal is to characterize the quantum state as well as possible despite the lack of a shared reference frame. Interestingly, although the correlation value of the outcomes of both observers (which quantifies the probability for both results being equal or opposite) is random as it depends on the respective measurement ...
