Determining complementary properties using weak-measurement: uncertainty, predictability, and disturbance
It is often said that measuring a system’s position must disturb the complementary property, momentum, by some minimum amount due to the Heisenberg uncertainty principle. Using a ‘weak-measurement’, this disturbance can be reduced. One might expect this comes at the cost of also reducing the measure...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2018-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/aaecdf |
| _version_ | 1797750556175892480 |
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| author | G S Thekkadath F Hufnagel J S Lundeen |
| author_facet | G S Thekkadath F Hufnagel J S Lundeen |
| author_sort | G S Thekkadath |
| collection | DOAJ |
| description | It is often said that measuring a system’s position must disturb the complementary property, momentum, by some minimum amount due to the Heisenberg uncertainty principle. Using a ‘weak-measurement’, this disturbance can be reduced. One might expect this comes at the cost of also reducing the measurement’s precision. However, it was recently demonstrated that a sequence consisting of a weak position measurement followed by a regular momentum measurement can probe a quantum system at a single point, with zero width, in position-momentum space. Here, we study this ‘joint weak-measurement’ and reconcile its compatibility with the uncertainty principle. While a single trial probes the system with a resolution that can saturate Heisenberg’s limit, we show that averaging over many trials can be used to surpass this limit. The weak-measurement does not trade away precision, but rather another type of uncertainty called ‘predictability’ which quantifies the certainty of retrodicting the measurement’s outcome. |
| first_indexed | 2024-03-12T16:35:29Z |
| format | Article |
| id | doaj.art-63ec145d8982415eabdc1aa8954f40eb |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:35:29Z |
| publishDate | 2018-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-63ec145d8982415eabdc1aa8954f40eb2023-08-08T14:55:40ZengIOP PublishingNew Journal of Physics1367-26302018-01-01201111303410.1088/1367-2630/aaecdfDetermining complementary properties using weak-measurement: uncertainty, predictability, and disturbanceG S Thekkadath0F Hufnagel1J S Lundeen2Clarendon Laboratory, University of Oxford , Parks Road, Oxford, OX1 3PU, United KingdomDepartment of Physics and Centre for Research in Photonics, University of Ottawa , 25 Templeton Street, Ottawa, Ontario, K1N 6N5, CanadaDepartment of Physics and Centre for Research in Photonics, University of Ottawa , 25 Templeton Street, Ottawa, Ontario, K1N 6N5, CanadaIt is often said that measuring a system’s position must disturb the complementary property, momentum, by some minimum amount due to the Heisenberg uncertainty principle. Using a ‘weak-measurement’, this disturbance can be reduced. One might expect this comes at the cost of also reducing the measurement’s precision. However, it was recently demonstrated that a sequence consisting of a weak position measurement followed by a regular momentum measurement can probe a quantum system at a single point, with zero width, in position-momentum space. Here, we study this ‘joint weak-measurement’ and reconcile its compatibility with the uncertainty principle. While a single trial probes the system with a resolution that can saturate Heisenberg’s limit, we show that averaging over many trials can be used to surpass this limit. The weak-measurement does not trade away precision, but rather another type of uncertainty called ‘predictability’ which quantifies the certainty of retrodicting the measurement’s outcome.https://doi.org/10.1088/1367-2630/aaecdfdirect measurementweak-measurementHeisenberg uncertainty principlejoint measurementmeasurement disturbancecomplementarity |
| spellingShingle | G S Thekkadath F Hufnagel J S Lundeen Determining complementary properties using weak-measurement: uncertainty, predictability, and disturbance New Journal of Physics direct measurement weak-measurement Heisenberg uncertainty principle joint measurement measurement disturbance complementarity |
| title | Determining complementary properties using weak-measurement: uncertainty, predictability, and disturbance |
| title_full | Determining complementary properties using weak-measurement: uncertainty, predictability, and disturbance |
| title_fullStr | Determining complementary properties using weak-measurement: uncertainty, predictability, and disturbance |
| title_full_unstemmed | Determining complementary properties using weak-measurement: uncertainty, predictability, and disturbance |
| title_short | Determining complementary properties using weak-measurement: uncertainty, predictability, and disturbance |
| title_sort | determining complementary properties using weak measurement uncertainty predictability and disturbance |
| topic | direct measurement weak-measurement Heisenberg uncertainty principle joint measurement measurement disturbance complementarity |
| url | https://doi.org/10.1088/1367-2630/aaecdf |
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