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The possible state space dimension increases exponentially with respect to the number of qubits. This feature makes the quantum state tomography expensive and impractical for identifying the state of merely several qubits. The recent developed approach, compressed sensing, gives us an alternative to estimate the quantum state with fewer measurements. It is proved that the estimation then can be converted to a convex optimization problem with quantum mechanics constraints. In this paper wearXiv:1401.6533v1 fatcat:7l3owt5dm5gd3h2n7ojhyz5564