In a paper arXiv:1312.0158 the authors proved that any complex vector (thus also the quantum state vector) can be uniquely determined (up to a global phase factor) by 4N-4 generic intensity measurements, where N is the dimension of the complex space. Thus if one can from an experiment obtain the absolute values of inner products of the state vector with 4N-4 other vectors that constitute a generic frame, then he is able to find the state vector. My question is: is it really experimentally doable to find such a number of projections of the state vector?

http://arxiv.org/abs/1312.0158

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