Fluctuations in the Number of Quantum States on Quantum Tomography Using Quasi-Quantum Cloned State

According to the no-cloning theorem, it is impossible to create an identical copy of an arbitrary unknown quantum state. Thus, performing a measurement on an unknown quantum state will collapse the state. In quantum state tomography, where the goal is to reconstruct the quantum state, it is necessary to generate a number of identical unknown quantum states equal to the number of measurements needed. Therefore, the number of quantum states that must be generated coincides with the number of samples required for the tomography process. In this study, we confirmed that the above relationship fluctuates stochastically by using the fact that a special unitary operation, which produces the pseudo-cloning of the quantum state, can be applied to restore the original quantum state stochastically after the measurement. This stochastic fluctuation suggests that, compared to existing methods, there exists the case where more information can be extracted than expected from the number of unknown quantum states to be prepared. We also verified numerical experiments with quantum gate by replacing the above scheme with a multi-qubit system, and showed that this scheme is realistically feasible.