1212.2815 (Antonio Di Lorenzo)

Measuring with correlated detectors: violation of Heisenberg
noise-disturbance principle and other surprises    [PDF]

Antonio Di Lorenzo

Heisenberg formulated an uncertainty 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. Heisenberg provided semiquantitative examples to support his conjecture, but no proof. Are these formulations of the uncertainty relation mathematically sound? Here, we answer this question by analyzing two nondemolition measurements of position and momentum and describing the quantum state of the detectors. The former literature neglected the possibility of pre-existing correlations between the two detectors. In case these are initially correlated, we prove the Heisenberg noise-disturbance principle not to hold. Furthermore, Ozawa and Arthurs-Kelly inequalities are also violated. Finally, we show that, by preceding a momentum measurement with a position measurement, the noise cancels out if the two probes are in an appropriate EPR state.

View original: http://arxiv.org/abs/1212.2815