Fundamental quantum limit to external force detection via monitoring a single harmonic oscillator or free mass

We show that there is a fundamental quantum limit to external force detection via monitoring a single harmonic oscillator, which was neglected so far. This limit is equivalent to the impossibility of determining the quantum state of a single oscillator, and the quantum Zeno effect of the oscillator, and requires an exchange of at least a quantum of energy between the oscillator and the force.