Demonstration of Complete Information Trade-Off in Quantum Measurement.

While an information-disturbance trade-off in quantum measurement has been at the core of foundational quantum physics and constitutes a basis of secure quantum information processing, recently verified reversibility of a quantum measurement requires to refine it toward a complete version of information trade-off in quantum measurement. Here we experimentally demonstrate a trade-off relation among all information contents, i.e., information gain, disturbance, and reversibility in quantum measurement. By exploring 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 triplewise all at once, and find that the triplewise 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.