Optimal Covariant Measurement of Momentum on a Half Line in Quantum Mechanics

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dc.creatorShikano, Yutaka
dc.creatorHosoya, Akio
dc.date2007-10-09
dc.date2008-05-07
dc.date.accessioned2026-07-07T09:40:34Z
dc.date.available2026-07-07T09:40:34Z
dc.descriptionWe cannot perform the projective measurement of a momentum on a half line since it is not an observable. Nevertheless, we would like to obtain some physical information of the momentum on a half line. We define an optimality for measurement as minimizing the variance between an inferred outcome of the measured system before a measuring process and a measurement outcome of the probe system after the measuring process, restricting our attention to the covariant measurement studied by Holevo. Extending the domain of the momentum operator on a half line by introducing a two dimensional Hilbert space to be tensored, we make it self-adjoint and explicitly construct a model Hamiltonian for the measured and probe systems. By taking the partial trace over the newly introduced Hilbert space, the optimal covariant positive operator valued measure (POVM) of a momentum on a half line is reproduced. We physically describe the measuring process to optimally evaluate the momentum of a particle on a half line.
dc.description12 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/0710.1724
dc.identifierhttp://arxiv.org/abs/0710.1724
dc.identifierJ. Math. Phys. 49, 052104 (2008)
dc.identifierdoi:10.1063/1.2917064
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/161524
dc.subjectQuantum Physics
dc.titleOptimal Covariant Measurement of Momentum on a Half Line in Quantum Mechanics
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