Global triplewise information trade-off in quantum measurement

Abstract

State disturbance by a quantum measurement is at the core of foundational quantum physics and constitutes a fundamental basis of secure quantum information processing. While quantifying an information-disturbance relation has been a long-standing problem, recently verified reversibility of a quantum measurement requires to refine such a conventional information trade-off toward a complete picture of information conservation in quantum measurement. Here we experimentally demonstrate complete trade-off relations among all information contents, i.e., information gain, disturbance and reversibility in quantum measurement. By exploring various quantum measurements applied on a photonic qutrit, we observe that the information of a quantum state is split into three distinct parts accounting for the extracted, disturbed, and reversible information. We verify that such different parts of information are in trade-off relations not only pairwise but also globally all-at-once, and find that the global trade-off relation is tighter than any of the pairwise relations. Finally, we realize optimal quantum measurements that inherently preserve quantum information without loss of information, which offer wider applications in measurement-based quantum information processing.