Proof of the Standard Quantum Limit for Monitoring Free-Mass Position

Abstract

The measurement result of the moved distance for a free mass m during the time t between two position measurements cannot be predicted with uncertainty smaller than sqrt{hbar t/2m}. This is formulated as a standard quantum limit (SQL) and it has been proven to always hold for the following position measurement: a probe is set in a prescribed position before the measurement. Just after the interaction of the mass with the probe, the probe position is measured, and using this value, the measurement results of the pre-measurement and post-measurement positions are estimated.

4 pages, no figure

References in corpus (3)

• Physical content of Heisenberg's uncertainty relation: Limitation and reformulation
• Position measuring interactions and the Heisenberg uncertainty principle
• Position Uncertainty in the Heisenberg Uncertainty Relation