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Measurement-induced back action, a direct consequence of the Heisenberg Uncertainty Principle, is the defining feature of quantum measurements. We use quantum measurement theory to analyze the recent experiment of Safavi-Naeini et al. [Phys. Rev. Lett. {bf 108}, 033602 (2012)], and show that results of this experiment not only characterize the zero-point fluctuation of a near-ground-state nanomechanical oscillator, but also demonstrate the existence of quantum back-action noise --- through correlations that exist between sensing noise and back-action noise. These correlations arise from the quantum coherence between the mechanical oscillator and the measuring device, which build up during the measurement process, and are key to improving sensitivities beyond the Standard Quantum Limit.
The quantum measurement of any observable naturally leads to noise added by the act of measurement. Approaches to evade or reduce this noise can lead to substantial improvements in a wide variety of sensors, from laser interferometers to precision ma
When an observable is measured on an evolving coherent quantum system twice, the first measurement generally alters the statistics of the second one, which is known as measurement back-action. We introduce, and push to its theoretical and experimenta
The standard quantum limit constrains the precision of an oscillator position measurement. It arises from a balance between the imprecision and the quantum back-action of the measurement. However, a measurement of only a single quadrature of the osci
Quantum mechanics postulates that measuring the qubits wave function results in its collapse, with the recorded discrete outcome designating the particular eigenstate that the qubit collapsed into. We show that this picture breaks down when the qubit
Quantum mechanics dictates that a continuous measurement of the position of an object imposes a random back action perturbation on its momentum. This randomness translates with time into position uncertainty, thus leading to the well known uncertaint