Quantum Physics

The theory of relativity associates a proper time with each moving object via its spacetime trajectory. In quantum theory on the other hand, such trajectories are forbidden. I will discuss an operation approach to exploring this conflict, considering the average time measured by a quantum clock in the weak-field, low-velocity limit. Considering the role of the clock’s state of motion, one finds that all ``good'' quantum clocks experience the time dilation prescribed by general relativity for the most classical states of motion. For nonclassical states of motion, on the other hand, one finds that quantum interference effects give rise to a discrepancy between the proper time and the time measured by the clock. I will also describe how ignorance of the clock's state of motion leads to a larger uncertainty in the time as measured by the clock, a consequence of entanglement between the clock time and its center-of-mass degrees of freedom.

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, preads 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, accepted by Comms. Phys. (in press) arXiv:1806.04147.