On an Internal Dependence of Simultaneous Measurements
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929317067358208 |
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| author | Iliev, Valentin Vankov |
| author_facet | Iliev, Valentin Vankov |
| contents | In this paper we show that there exists an internal dependence of the simultaneous measurements made by the two pairs of linear polarizers operated in each leg of the apparatus in Aspect's version of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment. The corresponding Shannon-Kolmogorov's information flow linking a polarizer from one leg to a polarizer from the other leg is proportional to the absolute value of this function of dependence. It turns out that if Bell's inequality is violated, then this information flow is strictly positive, that is, the experiment performed at one leg is informationally dependent on the experiment at the other leg. By throwing out the sign of absolute value, we define the signed information flow linking a polarizer from one leg to a polarizer from the other leg which, in turn, reproduces the probabilities of the four outcomes of the simultaneous measurements, predicted by quantum mechanics. We make an attempt to illustrate the seeming random relation between the total information flow, the total signed information flow, and the violation of Bell's inequality in terms of a kind of uncertainty principle. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_11263 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On an Internal Dependence of Simultaneous Measurements Iliev, Valentin Vankov Mathematical Physics In this paper we show that there exists an internal dependence of the simultaneous measurements made by the two pairs of linear polarizers operated in each leg of the apparatus in Aspect's version of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment. The corresponding Shannon-Kolmogorov's information flow linking a polarizer from one leg to a polarizer from the other leg is proportional to the absolute value of this function of dependence. It turns out that if Bell's inequality is violated, then this information flow is strictly positive, that is, the experiment performed at one leg is informationally dependent on the experiment at the other leg. By throwing out the sign of absolute value, we define the signed information flow linking a polarizer from one leg to a polarizer from the other leg which, in turn, reproduces the probabilities of the four outcomes of the simultaneous measurements, predicted by quantum mechanics. We make an attempt to illustrate the seeming random relation between the total information flow, the total signed information flow, and the violation of Bell's inequality in terms of a kind of uncertainty principle. |
| title | On an Internal Dependence of Simultaneous Measurements |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2404.11263 |