Complex counterpart of variance in quantum measurements for pre- and postselected systems
The variance of an observable in a preselected quantum system, which is always real and non-negative, appears as an increase in the probe wave packet width in indirect measurements. Extending this framework to pre- and postselected systems, we formulate a complex-valued counterpart of the variance c...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2021-07-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.3.033077 |
| _version_ | 1797210973649502208 |
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| author | Kazuhisa Ogawa Natsuki Abe Hirokazu Kobayashi Akihisa Tomita |
| author_facet | Kazuhisa Ogawa Natsuki Abe Hirokazu Kobayashi Akihisa Tomita |
| author_sort | Kazuhisa Ogawa |
| collection | DOAJ |
| description | The variance of an observable in a preselected quantum system, which is always real and non-negative, appears as an increase in the probe wave packet width in indirect measurements. Extending this framework to pre- and postselected systems, we formulate a complex-valued counterpart of the variance called “weak variance.” In our formulation, the real and imaginary parts of the weak variance appear as changes in the probe wave packet width in the vertical-horizontal and diagonal-antidiagonal directions, respectively, on the quadrature phase plane. Using an optical system, we experimentally demonstrate these changes in the probe wave packet width caused by the real negative and purely imaginary weak variances. Furthermore, we show that the weak variance can be expressed as the variance of the weak-valued probability distribution in pre- and postselected systems. These operational and statistical interpretations support the rationality of formulating the weak variance as a complex counterpart of the variance in pre- and postselected systems. |
| first_indexed | 2024-04-24T10:19:06Z |
| format | Article |
| id | doaj.art-1512c411353042d3ab0265dd0a506107 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:19:06Z |
| publishDate | 2021-07-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-1512c411353042d3ab0265dd0a5061072024-04-12T17:12:04ZengAmerican Physical SocietyPhysical Review Research2643-15642021-07-013303307710.1103/PhysRevResearch.3.033077Complex counterpart of variance in quantum measurements for pre- and postselected systemsKazuhisa OgawaNatsuki AbeHirokazu KobayashiAkihisa TomitaThe variance of an observable in a preselected quantum system, which is always real and non-negative, appears as an increase in the probe wave packet width in indirect measurements. Extending this framework to pre- and postselected systems, we formulate a complex-valued counterpart of the variance called “weak variance.” In our formulation, the real and imaginary parts of the weak variance appear as changes in the probe wave packet width in the vertical-horizontal and diagonal-antidiagonal directions, respectively, on the quadrature phase plane. Using an optical system, we experimentally demonstrate these changes in the probe wave packet width caused by the real negative and purely imaginary weak variances. Furthermore, we show that the weak variance can be expressed as the variance of the weak-valued probability distribution in pre- and postselected systems. These operational and statistical interpretations support the rationality of formulating the weak variance as a complex counterpart of the variance in pre- and postselected systems.http://doi.org/10.1103/PhysRevResearch.3.033077 |
| spellingShingle | Kazuhisa Ogawa Natsuki Abe Hirokazu Kobayashi Akihisa Tomita Complex counterpart of variance in quantum measurements for pre- and postselected systems Physical Review Research |
| title | Complex counterpart of variance in quantum measurements for pre- and postselected systems |
| title_full | Complex counterpart of variance in quantum measurements for pre- and postselected systems |
| title_fullStr | Complex counterpart of variance in quantum measurements for pre- and postselected systems |
| title_full_unstemmed | Complex counterpart of variance in quantum measurements for pre- and postselected systems |
| title_short | Complex counterpart of variance in quantum measurements for pre- and postselected systems |
| title_sort | complex counterpart of variance in quantum measurements for pre and postselected systems |
| url | http://doi.org/10.1103/PhysRevResearch.3.033077 |
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