Uncertainty Relation between Detection Probability and Energy Fluctuations
A classical random walker starting on a node of a finite graph will always reach any other node since the search is ergodic, namely it fully explores space, hence the arrival probability is unity. For quantum walks, destructive interference may induce effectively non-ergodic features in such search...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-05-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/5/595 |
| _version_ | 1797534535169081344 |
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| author | Felix Thiel Itay Mualem David Kessler Eli Barkai |
| author_facet | Felix Thiel Itay Mualem David Kessler Eli Barkai |
| author_sort | Felix Thiel |
| collection | DOAJ |
| description | A classical random walker starting on a node of a finite graph will always reach any other node since the search is ergodic, namely it fully explores space, hence the arrival probability is unity. For quantum walks, destructive interference may induce effectively non-ergodic features in such search processes. Under repeated projective local measurements, made on a target state, the final detection of the system is not guaranteed since the Hilbert space is split into a bright subspace and an orthogonal dark one. Using this we find an uncertainty relation for the deviations of the detection probability from its classical counterpart, in terms of the energy fluctuations. |
| first_indexed | 2024-03-10T11:31:57Z |
| format | Article |
| id | doaj.art-a27a97b6245241aebb4185ed63fc10f8 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T11:31:57Z |
| publishDate | 2021-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-a27a97b6245241aebb4185ed63fc10f82023-11-21T19:12:00ZengMDPI AGEntropy1099-43002021-05-0123559510.3390/e23050595Uncertainty Relation between Detection Probability and Energy FluctuationsFelix Thiel0Itay Mualem1David Kessler2Eli Barkai3Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, IsraelDepartment of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, IsraelDepartment of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, IsraelDepartment of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, IsraelA classical random walker starting on a node of a finite graph will always reach any other node since the search is ergodic, namely it fully explores space, hence the arrival probability is unity. For quantum walks, destructive interference may induce effectively non-ergodic features in such search processes. Under repeated projective local measurements, made on a target state, the final detection of the system is not guaranteed since the Hilbert space is split into a bright subspace and an orthogonal dark one. Using this we find an uncertainty relation for the deviations of the detection probability from its classical counterpart, in terms of the energy fluctuations.https://www.mdpi.com/1099-4300/23/5/595quantum searchdark and bright statesZeno subspacesergodicity |
| spellingShingle | Felix Thiel Itay Mualem David Kessler Eli Barkai Uncertainty Relation between Detection Probability and Energy Fluctuations Entropy quantum search dark and bright states Zeno subspaces ergodicity |
| title | Uncertainty Relation between Detection Probability and Energy Fluctuations |
| title_full | Uncertainty Relation between Detection Probability and Energy Fluctuations |
| title_fullStr | Uncertainty Relation between Detection Probability and Energy Fluctuations |
| title_full_unstemmed | Uncertainty Relation between Detection Probability and Energy Fluctuations |
| title_short | Uncertainty Relation between Detection Probability and Energy Fluctuations |
| title_sort | uncertainty relation between detection probability and energy fluctuations |
| topic | quantum search dark and bright states Zeno subspaces ergodicity |
| url | https://www.mdpi.com/1099-4300/23/5/595 |
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