Correlations between detectors allow violation of the Heisenberg noise-disturbance principle for position and momentum measurements

TL;DR

This paper demonstrates that the traditional Heisenberg noise-disturbance principle for position and momentum measurements can be violated when detectors are initially correlated, challenging a fundamental quantum measurement limit.

Contribution

It provides a theoretical proof that the Heisenberg sequential noise-disturbance principle can be violated with correlated detectors, expanding understanding of measurement limitations.

Findings

Heisenberg principle holds for uncorrelated detectors

Correlated initial detector states can violate the principle

Implications for quantum measurement theory

Abstract

Heisenberg formulated a noise-disturbance principle stating that there is a tradeoff between noise and disturbance when a measurement of position and a measurement of momentum are performed sequentially, and another principle imposing a limitation on the product of the uncertainties in a joint measurement of position and momentum. We prove that the former, the Heisenberg sequential noise-disturbance principle, holds when the detectors are assumed to be initially uncorrelated from each other, but that it can be violated for some properly correlated initial preparations of the detectors.