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• W3105324873 abstract "In a previous paper we have presented a general scheme for the implementation of symmetric generalized measurements (POVMs) on a quantum computer. This scheme is based on representation theory of groups and methods to decompose matrices that intertwine two representations. We extend this scheme in such a way that the measurement is minimally disturbing, i.e., it changes the state vector ket{Psi} of the system to sqrt{Pi} ket{Psi} where Pi is the positive operator corresponding to the measured result. Using this method, we construct quantum circuits for measurements with Heisenberg-Weyl symmetry. A continuous generalization leads to a scheme for optimal simultaneous measurements of position and momentum of a Schrodinger particle moving in one dimension such that the outcomes satisfy Delta x Delta p geq hbar. The particle to be measured collides with two probe particles, one for the position and the other for the momentum measurement. The position and momentum resolution can be tuned by the entangled joint state of the probe particles which is also generated by a collision with hard-core potential. The parameters of the POVM can then be controlled by the initial widths of the wave functions of the probe particles. We point out some formal similarities and differences to simultaneous measurements of quadrature amplitudes in quantum optics." @default.
• W3105324873 created "2020-11-23" @default.
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• W3105324873 date "2006-08-01" @default.
• W3105324873 modified "2023-10-16" @default.
• W3105324873 title "Minimally disturbing Heisenberg–Weyl symmetric measurements using hard-core collisions of Schrödinger particles" @default.
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• W3105324873 doi "https://doi.org/10.1063/1.2222080" @default.
• W3105324873 hasPublicationYear "2006" @default.
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