Approximate joint measurement of qubit observables through an Arthur-Kelly type model

Details Approximate joint measurement of qubit observables through an Arthur-Kelly type model Approximate joint measurement of qubit observables through an Arthur-Kelly type model

2010-10-14

arxiv.org/abs/1010.2878v1

Physics

Quantum Physics

22 pages; Latex

Scientific paper

We consider joint measurement of two and three unsharp qubit observables through an Arthur-Kelly type joint measurement model for qubits. We investigate the effect of initial state of the detectors on quality of the the POVMs of the measurement as well as the post-measurement state of the system. Two approaches for characterising the quality of unsharp measurement and the resulting measurement uncertainty relations are considered.The corresponding measures of unsharpness are connected for the case where both the measurements are equally unsharp. The connection between the POVM elements and symmetries of the underlying Hamiltonian of the measurement interaction is made explicit and used to perform joint measurement in arbitrary directions. Finally, in the case of three observables, we derive a necessary condition for the approximate joint measurement and use it show the relative freedom available when the observables are non-orthogonal.

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