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We propose a protocol to improve the accuracy of direct complex statemeasurements (DSM) by using rebits in real Hilbert spaces. We show that toimprove the accuracy, the initial complex state should be decomposed into thereal and imaginary parts and stored in an extended state (rebit) which can betracked individually by two bases of an extra qubit. For pure states, thenumerical calculations show that the trace distances between the true state andthe reconstructed state obtained from the rebit method are more precise thanthose ones obtained from the usual DSM and quantum state tomography (SQT)because the number of projective measurements is reduced. For mixed states, therebit method gives the same accuracy in comparison to the usual DSM, while itis less precise than QST. Its precision is also significantly improved whenusing nearly-pure states. Our proposal holds promises as a reliable tool forquantum computation, testing of quantum circuits by using only real amplitudes.

Improving direct state measurements by using rebits in real enlarged Hilbert spaces