Davide Girolami, Tommaso Tufarelli, Gerardo Adesso
Quantum mechanics predicts that measurements of incompatible observables carry an uncertainty which is independent of technical deficiencies of the measurement apparatus or incomplete knowledge of the state of the system. Nothing yet seems to prevent a single physical quantity, such as one spin component, from being measured with arbitrary precision. Here we show that an intrinsic quantum uncertainty on a single observable is ineludible in a number of physical situations. In spite of affecting the statistics of measurement outcomes elusively, such uncertainty is a quantum hypernym: it yields the most general form of quantum correlations, provides a statistical interpretation of quantum symmetries and modulates Heisenberg uncertainty relations. We further find that quantum uncertainty on single local observables is a resource for quantum metrology tasks, as it can be exploited to improve the efficiency of parameter estimation with noisy probes.
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http://arxiv.org/abs/1212.2214
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