Adaptive quantum tomography in an indistinct measurement system with superconducting circuits
Hyeok Hwang, JeaKyung Choi, Eunseong Kim · Physical Review Applied · 2023
Adaptive tomography has been widely investigated with the aim of achieving faster state tomography processing of quantum systems. Infidelity of the nearly pure states in a quantum information process generally scales as $O(1/\sqrt{N})$, which requires a large number of statistical ensembles in comparison to the infidelity scaling of $O(1/N)$ for mixed states. One previous report optimized the measurement basis in a photonic qubit system, whose state tomography uses projective measurements, to obtain an infidelity scaling of $O(1/N)$. However, this dramatic improvement cannot be applied to indistinct measurement systems in which two quantum states cannot be distinguished with perfect measurement fidelity. We introduce in this work an optimal measurement basis to achieve fast adaptive quantum state tomography and a minimum magnitude of infidelity in an indistinct measurement system. We expect that the adaptive quantum state tomography protocol can lead to a reduction in the number of required measurements of approximately 33.74% via analytical expectation without changing the $O(1/\sqrt{N})$ scaling. Experimentally, we find a 15.06% measurement number reduction in a superconducting circuit system.