General wisdom tells us that if two quantum states are ``macroscopicallydistinguishable'' then their superposition should be hard to observe. We makethis intuition precise and general by quantifying the difficulty to observe thequantum nature of a superposition of two states that can be distinguishedwithout microscopic accuracy. First, we quantify the distinguishability of anygiven pair of quantum states with measurement devices lacking microscopicaccuracy, i.e. measurements suffering from limited resolution or limitedsensitivity. Next, we quantify the required stability that have to be fulfilledby any measurement setup able to distinguish their superposition from a meremixture. Finally, by establishing a relationship between the stabilityrequirement and the ``macroscopic distinguishability'' of the two superposedstates, we demonstrate that indeed, the more distinguishable the states are,the more demanding are the stability requirements.
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