Quantum Measurements, Stochastic Networks, the Uncertainty Principle, and the Not So Strange “Weak Values”
Suppose we make a series of measurements on a chosen quantum system. The outcomes of the measurements form a sequence of random events, which occur in a particular order. The system, together with a meter or meters, can be seen as following the paths of a stochastic network connecting all possible o...
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| Format: | Article |
| Language: | English |
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MDPI AG
2016-09-01
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| Series: | Mathematics |
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| Online Access: | http://www.mdpi.com/2227-7390/4/3/56 |
| _version_ | 1818365296323330048 |
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| author | Dmitri Sokolovski |
| author_facet | Dmitri Sokolovski |
| author_sort | Dmitri Sokolovski |
| collection | DOAJ |
| description | Suppose we make a series of measurements on a chosen quantum system. The outcomes of the measurements form a sequence of random events, which occur in a particular order. The system, together with a meter or meters, can be seen as following the paths of a stochastic network connecting all possible outcomes. The paths are shaped from the virtual paths of the system, and the corresponding probabilities are determined by the measuring devices employed. If the measurements are highly accurate, the virtual paths become “real”, and the mean values of a quantity (a functional) are directly related to the frequencies with which the paths are traveled. If the measurements are highly inaccurate, the mean (weak) values are expressed in terms of the relative probabilities’ amplitudes. For pre- and post-selected systems they are bound to take arbitrary values, depending on the chosen transition. This is a direct consequence of the uncertainty principle, which forbids one from distinguishing between interfering alternatives, while leaving the interference between them intact. |
| first_indexed | 2024-12-13T22:18:00Z |
| format | Article |
| id | doaj.art-309925a40d4841369d354fa7e8e2b8d4 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-13T22:18:00Z |
| publishDate | 2016-09-01 |
| publisher | MDPI AG |
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| spelling | doaj.art-309925a40d4841369d354fa7e8e2b8d42022-12-21T23:29:27ZengMDPI AGMathematics2227-73902016-09-01435610.3390/math4030056math4030056Quantum Measurements, Stochastic Networks, the Uncertainty Principle, and the Not So Strange “Weak Values”Dmitri Sokolovski0Departamento de Química-Física, Universidad del País Vasco, UPV/EHU, Leioa 48940, Bizkaia, SpainSuppose we make a series of measurements on a chosen quantum system. The outcomes of the measurements form a sequence of random events, which occur in a particular order. The system, together with a meter or meters, can be seen as following the paths of a stochastic network connecting all possible outcomes. The paths are shaped from the virtual paths of the system, and the corresponding probabilities are determined by the measuring devices employed. If the measurements are highly accurate, the virtual paths become “real”, and the mean values of a quantity (a functional) are directly related to the frequencies with which the paths are traveled. If the measurements are highly inaccurate, the mean (weak) values are expressed in terms of the relative probabilities’ amplitudes. For pre- and post-selected systems they are bound to take arbitrary values, depending on the chosen transition. This is a direct consequence of the uncertainty principle, which forbids one from distinguishing between interfering alternatives, while leaving the interference between them intact.http://www.mdpi.com/2227-7390/4/3/56quantum probabilitiesuncertainty principletransition amplitudes“weak values” |
| spellingShingle | Dmitri Sokolovski Quantum Measurements, Stochastic Networks, the Uncertainty Principle, and the Not So Strange “Weak Values” Mathematics quantum probabilities uncertainty principle transition amplitudes “weak values” |
| title | Quantum Measurements, Stochastic Networks, the Uncertainty Principle, and the Not So Strange “Weak Values” |
| title_full | Quantum Measurements, Stochastic Networks, the Uncertainty Principle, and the Not So Strange “Weak Values” |
| title_fullStr | Quantum Measurements, Stochastic Networks, the Uncertainty Principle, and the Not So Strange “Weak Values” |
| title_full_unstemmed | Quantum Measurements, Stochastic Networks, the Uncertainty Principle, and the Not So Strange “Weak Values” |
| title_short | Quantum Measurements, Stochastic Networks, the Uncertainty Principle, and the Not So Strange “Weak Values” |
| title_sort | quantum measurements stochastic networks the uncertainty principle and the not so strange weak values |
| topic | quantum probabilities uncertainty principle transition amplitudes “weak values” |
| url | http://www.mdpi.com/2227-7390/4/3/56 |
| work_keys_str_mv | AT dmitrisokolovski quantummeasurementsstochasticnetworkstheuncertaintyprincipleandthenotsostrangeweakvalues |