DisturbanceDisturbance uncertainty relation: The statistical distinguishability of quantum states determines disturbance
Abstract
The Heisenberg uncertainty principle, which underlies many quantum key features, is under close scrutiny regarding its applicability to new scenarios. Using both the BellKochenSpecker theorem establishing that observables do not have predetermined values before measurements and the measurement postulate of quantum mechanics, we propose that in order to describe the disturbance produced by the measurement process, it is convenient to define disturbance by the changes produced on quantum states. Hence, we propose to quantify disturbance in terms of the square root of the JensenShannon entropy distance between the probability distributions before and after the measurement process. Additionally, disturbance and statistical distinguishability of states are fundamental concepts of quantum mechanics that have thus far been unrelated; however, we show that they are intermingled thereupon we enquire into whether the statistical distinguishability of states, caused by statistical fluctuations in the measurement outcomes, is responsible for the disturbance's magnitude.
 Publication:

Scientific Reports
 Pub Date:
 March 2018
 DOI:
 10.1038/s41598018223363
 Bibcode:
 2018NatSR...8.4010B