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Trajectories without quantum uncertainties

A common knowledge suggests that trajectories of particles in quantum mechanics always have quantum uncertainties. These quantum uncertainties set by the Heisenberg uncertainty principle limit precision of measurements of fields and forces, and ultimately give rise to the standard quantum limit in metrology. With the rapid developments of sensitivity of measurements these limits have been approached in various types of measurements including measurements of fields and acceleration. Here we show that a quantum trajectory of one system measured relatively to the other "reference system" with an effective negative mass can be quantum uncertainty--free. The method crucially relies on the generation of an Einstein-Podolsky-Rosen entangled state of two objects, one of which has an effective negative mass. From a practical perspective these ideas open the way towards force and acceleration measurements at new levels of sensitivity far below the standard quantum limit.