Error and Disturbance as Irreversibility with Applications: Unified Definition, Wigner--Araki--Yanase Theorem and Out-of-Time-Order Correlator

Haruki Emori, Hiroyasu Tajima

Published 2023-09-25Version 1

Error and disturbance are fundamental concepts in quantum measurements. Here we show that these two concepts can be defined as special cases of the irreversibility of quantum processes. The re-definitions provide fruitful byproducts: First, we can unify the existing various definitions of error and disturbance as special aspects of irreversibility. Second, we extend the quantitative Wigner--Araki--Yanase theorem -- a universal restriction on measurement implementation under a conservation law -- to error and disturbance of arbitrary definitions. Third, we provide a novel treatment of out-of-time-orderd-correlator (OTOC) -- a measure of quantum chaos in a quantum many-body system -- as irreversibility, and its experimental evaluation method.