Quantum Uncertainty and Error-Disturbance Tradeoff

TL;DR

This paper reexamines the quantum error-disturbance tradeoff, revealing it depends on the uncertainties of non-commuting observables and can be characterized by Jensen-Shannon divergence, challenging traditional views.

Contribution

It demonstrates that the error-disturbance tradeoff in quantum measurements is governed by the uncertainties of involved observables and introduces Jensen-Shannon divergence as a measure.

Findings

Tradeoff depends on the certainty of observables.

No tradeoff when one observable is more certain.

Jensen-Shannon divergence effectively characterizes the tradeoff.

Abstract

The uncertainty principle is often interpreted by the tradeoff between the error of a measurement and the consequential disturbance to the followed ones, which originated long ago from Heisenberg himself but now falls into reexamination and even heated debate. Here we show that the tradeoff is switched on or off by the quantum uncertainties of two involved non-commuting observables: if one is more certain than the other, there is no tradeoff; otherwise, they do have tradeoff and the Jensen-Shannon divergence gives it a good characterization.