= Preparation uncertainty
<Preparation uncertainty> describes the outcome spread intrinsic to a specified <quantum state preparation>. Operationally, prepare many copies of the same <quantum state>, measure <position> on one group and <momentum> on another, and estimate the two <variances>. Ideal measurements still have the spreads predicted by the <Born rule>. No earlier <position> measurement need occur in the <momentum> group. The <Heisenberg uncertainty relation> constrains these two distributions belonging to the same preparation.
<Measurement backaction> concerns how a particular <measurement in quantum mechanics> changes a <quantum state>. Instrument resolution concerns how its reported outcomes relate to the intended <observable>. Those questions require a model of the instrument and its interaction with the system. Substituting an instrument error and an induced change for $\Delta x$ and $\Delta p$ in the <Heisenberg uncertainty relation> does not follow from its proof. The practical value of <preparation uncertainty> is that it bounds achievable input spreads before any such instrument model is chosen.
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