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Gianfranco (talk | contribs) (Created page with "==4. Quantum instruments from the scheme of indirect measurements== The basic model for construction of quantum instruments is based on the scheme of indirect measurements. This scheme formalizes the following situation: measurement’s outputs are generated via interaction of a system <math>S</math> with a measurement apparatus <math>M</math> . This apparatus consists of a complex physical device interacting with <math>S</math> and a pointer that shows the result of me...") |
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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) as a “(general) measuring process”, is a quadruple | An ''indirect measurement model'', introduced in Ozawa (1984)<ref name=":0">Ozawa M. | ||
Quantum measuring processes for continuous observables | |||
J. Math. Phys., 25 (1984), pp. 79-87 Google Scholar</ref> as a “(general) measuring process”, is a quadruple | |||
<math>(H,\sigma,U,M_A)</math> | <math>(H,\sigma,U,M_A)</math> | ||
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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). Thus, quantum instruments mathematically characterize the statistical properties of all the physically realizable quantum measurements. | 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=":0" /><ref name=":0" /> Thus, quantum instruments mathematically characterize the statistical properties of all the physically realizable quantum measurements. | ||