Mean of continuous variables observable via measurement on single qubit
Abstract
It is shown that mean value of any observable with bounded spectrum can be uniquely determined from binary statistics of the measurement performed on single qubit ancilla coupled to a given system. The observable structure is fully encoded in the corresponding POVM. The method is generalised to the case of distant labs paradigm and discussed in the context of entanglement detection with few local measurements. The results are also discussed in the context of quantum programming.
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