Adaptive Quantum Tomography in a Non-Deterministic Measurement Environment Utilizing Superconducting Circuits

Adaptive tomography has been widely investigated to achieve faster state tomography processing of quantum systems. Infidelity of the nearly pure states in a quantum information process generally scales as O(1/√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 a new 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/√N) scaling. Experimentally, we find a 15.06% measurement number reduction in a superconducting circuit system.