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Difference between revisions of "Store:QLMen09"
→4. Quantum instruments from the scheme of indirect measurements
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# the meter observable <math>M_A</math> giving outputs of the pointer of the apparatus <math>M</math>. | # the meter observable <math>M_A</math> giving outputs of the pointer of the apparatus <math>M</math>. | ||
An ''indirect measurement model'', introduced in Ozawa (1984)<ref name=": | An ''indirect measurement model'', introduced in Ozawa (1984)<ref name=":Ozawa M (1984)">Ozawa M. Quantum measuring processes for continuous observables. J. Math. Phys., 25 (1984), pp. 79-87. Google Scholar</ref> | ||
Quantum measuring processes for continuous observables | Quantum measuring processes for continuous observables | ||
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where <math>Tr_\mathcal{H}</math> is the partial trace over <math>\mathcal{H}</math> . Then, the map <math>x\rightarrow\Im_A(x)</math>turn out to be a quantum instrument. Thus, the statistical properties of the measurement realized by any indirect measurement model <math>(H,\sigma,U,M_A)</math> is described by a quantum measurement. We remark that conversely any quantum instrument can be represented via the indirect measurement model (Ozawa, 1984).<ref name=": | where <math>Tr_\mathcal{H}</math> is the partial trace over <math>\mathcal{H}</math> . Then, the map <math>x\rightarrow\Im_A(x)</math>turn out to be a quantum instrument. Thus, the statistical properties of the measurement realized by any indirect measurement model <math>(H,\sigma,U,M_A)</math> is described by a quantum measurement. We remark that conversely any quantum instrument can be represented via the indirect measurement model (Ozawa, 1984).<ref name=":Ozawa M (1984)">Ozawa M. Quantum measuring processes for continuous observables. J. Math. Phys., 25 (1984), pp. 79-87. Google Scholar</ref>Thus, quantum instruments mathematically characterize the statistical properties of all the physically realizable quantum measurements. | ||