Reconciling two notions of quantum operator disagreement: Uncertainty relations and information scrambling
How violently do two quantum operators disagree? Different subfields of physics feature different notions of incompatibility: (i) In quantum information theory, uncertainty relations are cast in terms of entropies. These entropic uncertainty relations constrain measurement outcomes. (ii) Condensed matter and high-energy physics feature interacting quantum many-body systems, such as spin chains. A local perturbation, such as a Pauli operator on one side of a chain, spreads through many-body entanglement. The perturbation comes to overlap, and to disagree, with probes localized on the opposite side of the system. This disagreement signals that quantum information about the perturbation has scrambled, or become hidden in highly nonlocal correlations. I will unite these two notions of quantum operator disagreement, presenting an entropic uncertainty relation for quantum-information scrambling. The entropies are of distributions over weak and strong measurements’ possible outcomes. The uncertainty bound strengthens when a spin chain scrambles in numerical simulations. Hence the subfields—
quantum information, condensed matter, and high-energy physics—can agree about when quantum operations disagree. Our relation can be tested experimentally with superconducting qubits, trapped ions, and quantum dots.
NYH, Bartolotta, and Pollack, arXiv:1806.04147 (2018).