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An n-qubit quantum register can in principle be completely controlled byoperating on a single qubit that interacts with the register via an appropriatefixed interaction. We consider a hypothetical system consisting of n spin-1/2nuclei that interact with an electron spin via a magnetic interaction. Wedescribe algorithms that measure non-trivial joint observables on the registerby acting on the control spin only. For large n this is not an efficient modelfor universal quantum computation but it can be modified to an efficient one ifone allows n possible positions of the control particle.  This toy model of measurements illustrates in which way specific interactionsbetween the register and a probe particle support specific types of jointmeasurements in the sense that some joint observables can be measured by simplesequences of operations on the probe particle.Comment: 7 pages, revtex, 3 figure

Performing joint measurements and transformations on several qubits by operating on a single “control” qubit