Effects of the free evolution in the Arthurs–Kelly model of simultaneous measurement and in the retrodictive predictions of the Heisenberg uncertainty relations
Since its conception, the simultaneous measurement approach of Arthurs and Kelly has been a significant tool for the better understanding of the measurement process in quantum mechanics. This model considers a strong interaction Hamiltonian by discarding the free evolution part. In this work, we stu...
Gespeichert in:
| Veröffentlicht in: | European physical journal plus 2021-09, Vol.136 (9), p.954, Article 954 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | 9 |
| container_start_page | 954 |
| container_title | European physical journal plus |
| container_volume | 136 |
| creator | Mendoza-Fierro, J. A. Arévalo Aguilar, L. M. Velázquez Aguilar, V. M. |
| description | Since its conception, the simultaneous measurement approach of Arthurs and Kelly has been a significant tool for the better understanding of the measurement process in quantum mechanics. This model considers a strong interaction Hamiltonian by discarding the free evolution part. In this work, we study the effect of the full dynamics—taking into account the free Hamiltonian—on the optimal limits of retrodictive and predictive accuracy of the simultaneous measurement process of position and momentum observables. To do that, we consider a minimum uncertainty Gaussian state as the system under inspection, which allows to carry out an optimal simultaneous measurement. We show that the inclusion of the free Hamiltonian induces a spreading on the probability density of the measurement setting, which increases the value of the product of the variances of the so-called retrodictive and predictive error operators, this is equivalent to a reduction in the accuracy of the measurement. |
| doi_str_mv | 10.1140/epjp/s13360-021-01943-6 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2919501840</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2919501840</sourcerecordid><originalsourceid>FETCH-LOGICAL-c334t-c9804d1f912acb8fc07e294786854e7bfa11d93e66a31a3f8b09683e3cd3724d3</originalsourceid><addsrcrecordid>eNqFkU1OwzAQRiMEEhX0DFhiHWrHbhIvq6pQRCU2sLYcZ9ymSuxgO5W64w7cgKNxEtKUvx2zmdHoezOLF0VXBN8QwvAE2m078YTSFMc4ITEmnNE4PYlGCeE4njLGTv_M59HY-y3ui3HCOBtF7wutQQWPrEZhA0g7AAQ7W3ehsgZVZtjOXNh0zn-8vj1AXe9RY0uoD4ivmq4O0oDtPGpA-s5BAyYgacpv2EFwtqxUqHaAWgfDaM3PyyVUHkwBbo06o8AFWZmw77FaDrnL6EzL2sP4q19Ez7eLp_kyXj3e3c9nq1hRykKseI5ZSTQniVRFrhXOIOEsy9N8yiArtCSk5BTSVFIiqc4LzNOcAlUlzRJW0ovo-ni3dfalAx_E1nbO9C9FwgmfYpIz3KeyY0o5670DLVpXNdLtBcHi4EQcnIijE9E7EYMTkfZkfiR9T5g1uN_7_6GfdkWX6w</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2919501840</pqid></control><display><type>article</type><title>Effects of the free evolution in the Arthurs–Kelly model of simultaneous measurement and in the retrodictive predictions of the Heisenberg uncertainty relations</title><source>AUTh Library subscriptions: ProQuest Central</source><source>Springer Journals</source><creator>Mendoza-Fierro, J. A. ; Arévalo Aguilar, L. M. ; Velázquez Aguilar, V. M.</creator><creatorcontrib>Mendoza-Fierro, J. A. ; Arévalo Aguilar, L. M. ; Velázquez Aguilar, V. M.</creatorcontrib><description>Since its conception, the simultaneous measurement approach of Arthurs and Kelly has been a significant tool for the better understanding of the measurement process in quantum mechanics. This model considers a strong interaction Hamiltonian by discarding the free evolution part. In this work, we study the effect of the full dynamics—taking into account the free Hamiltonian—on the optimal limits of retrodictive and predictive accuracy of the simultaneous measurement process of position and momentum observables. To do that, we consider a minimum uncertainty Gaussian state as the system under inspection, which allows to carry out an optimal simultaneous measurement. We show that the inclusion of the free Hamiltonian induces a spreading on the probability density of the measurement setting, which increases the value of the product of the variances of the so-called retrodictive and predictive error operators, this is equivalent to a reduction in the accuracy of the measurement.</description><identifier>ISSN: 2190-5444</identifier><identifier>EISSN: 2190-5444</identifier><identifier>DOI: 10.1140/epjp/s13360-021-01943-6</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Accuracy ; Applied and Technical Physics ; Atomic ; Commuting ; Complex Systems ; Condensed Matter Physics ; Evolution ; Hamiltonian functions ; Mathematical and Computational Physics ; Measurement techniques ; Molecular ; Optical and Plasma Physics ; Physics ; Physics and Astronomy ; Position measurement ; Probability ; Quantum mechanics ; Quantum physics ; Regular Article ; Standard deviation ; Theoretical ; Uncertainty</subject><ispartof>European physical journal plus, 2021-09, Vol.136 (9), p.954, Article 954</ispartof><rights>The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021</rights><rights>The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c334t-c9804d1f912acb8fc07e294786854e7bfa11d93e66a31a3f8b09683e3cd3724d3</citedby><cites>FETCH-LOGICAL-c334t-c9804d1f912acb8fc07e294786854e7bfa11d93e66a31a3f8b09683e3cd3724d3</cites><orcidid>0000-0001-7603-3667</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1140/epjp/s13360-021-01943-6$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2919501840?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>314,776,780,21367,27901,27902,33721,41464,42533,43781,51294</link.rule.ids></links><search><creatorcontrib>Mendoza-Fierro, J. A.</creatorcontrib><creatorcontrib>Arévalo Aguilar, L. M.</creatorcontrib><creatorcontrib>Velázquez Aguilar, V. M.</creatorcontrib><title>Effects of the free evolution in the Arthurs–Kelly model of simultaneous measurement and in the retrodictive predictions of the Heisenberg uncertainty relations</title><title>European physical journal plus</title><addtitle>Eur. Phys. J. Plus</addtitle><description>Since its conception, the simultaneous measurement approach of Arthurs and Kelly has been a significant tool for the better understanding of the measurement process in quantum mechanics. This model considers a strong interaction Hamiltonian by discarding the free evolution part. In this work, we study the effect of the full dynamics—taking into account the free Hamiltonian—on the optimal limits of retrodictive and predictive accuracy of the simultaneous measurement process of position and momentum observables. To do that, we consider a minimum uncertainty Gaussian state as the system under inspection, which allows to carry out an optimal simultaneous measurement. We show that the inclusion of the free Hamiltonian induces a spreading on the probability density of the measurement setting, which increases the value of the product of the variances of the so-called retrodictive and predictive error operators, this is equivalent to a reduction in the accuracy of the measurement.</description><subject>Accuracy</subject><subject>Applied and Technical Physics</subject><subject>Atomic</subject><subject>Commuting</subject><subject>Complex Systems</subject><subject>Condensed Matter Physics</subject><subject>Evolution</subject><subject>Hamiltonian functions</subject><subject>Mathematical and Computational Physics</subject><subject>Measurement techniques</subject><subject>Molecular</subject><subject>Optical and Plasma Physics</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Position measurement</subject><subject>Probability</subject><subject>Quantum mechanics</subject><subject>Quantum physics</subject><subject>Regular Article</subject><subject>Standard deviation</subject><subject>Theoretical</subject><subject>Uncertainty</subject><issn>2190-5444</issn><issn>2190-5444</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><recordid>eNqFkU1OwzAQRiMEEhX0DFhiHWrHbhIvq6pQRCU2sLYcZ9ymSuxgO5W64w7cgKNxEtKUvx2zmdHoezOLF0VXBN8QwvAE2m078YTSFMc4ITEmnNE4PYlGCeE4njLGTv_M59HY-y3ui3HCOBtF7wutQQWPrEZhA0g7AAQ7W3ehsgZVZtjOXNh0zn-8vj1AXe9RY0uoD4ivmq4O0oDtPGpA-s5BAyYgacpv2EFwtqxUqHaAWgfDaM3PyyVUHkwBbo06o8AFWZmw77FaDrnL6EzL2sP4q19Ez7eLp_kyXj3e3c9nq1hRykKseI5ZSTQniVRFrhXOIOEsy9N8yiArtCSk5BTSVFIiqc4LzNOcAlUlzRJW0ovo-ni3dfalAx_E1nbO9C9FwgmfYpIz3KeyY0o5670DLVpXNdLtBcHi4EQcnIijE9E7EYMTkfZkfiR9T5g1uN_7_6GfdkWX6w</recordid><startdate>20210901</startdate><enddate>20210901</enddate><creator>Mendoza-Fierro, J. A.</creator><creator>Arévalo Aguilar, L. M.</creator><creator>Velázquez Aguilar, V. M.</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>AEUYN</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>BKSAR</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>P5Z</scope><scope>P62</scope><scope>PCBAR</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><orcidid>https://orcid.org/0000-0001-7603-3667</orcidid></search><sort><creationdate>20210901</creationdate><title>Effects of the free evolution in the Arthurs–Kelly model of simultaneous measurement and in the retrodictive predictions of the Heisenberg uncertainty relations</title><author>Mendoza-Fierro, J. A. ; Arévalo Aguilar, L. M. ; Velázquez Aguilar, V. M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c334t-c9804d1f912acb8fc07e294786854e7bfa11d93e66a31a3f8b09683e3cd3724d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Accuracy</topic><topic>Applied and Technical Physics</topic><topic>Atomic</topic><topic>Commuting</topic><topic>Complex Systems</topic><topic>Condensed Matter Physics</topic><topic>Evolution</topic><topic>Hamiltonian functions</topic><topic>Mathematical and Computational Physics</topic><topic>Measurement techniques</topic><topic>Molecular</topic><topic>Optical and Plasma Physics</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Position measurement</topic><topic>Probability</topic><topic>Quantum mechanics</topic><topic>Quantum physics</topic><topic>Regular Article</topic><topic>Standard deviation</topic><topic>Theoretical</topic><topic>Uncertainty</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Mendoza-Fierro, J. A.</creatorcontrib><creatorcontrib>Arévalo Aguilar, L. M.</creatorcontrib><creatorcontrib>Velázquez Aguilar, V. M.</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest One Sustainability</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Database (1962 - current)</collection><collection>AUTh Library subscriptions: ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest Natural Science Collection</collection><collection>Earth, Atmospheric & Aquatic Science Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>SciTech Premium Collection</collection><collection>ProQuest advanced technologies & aerospace journals</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Earth, Atmospheric & Aquatic Science Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><jtitle>European physical journal plus</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Mendoza-Fierro, J. A.</au><au>Arévalo Aguilar, L. M.</au><au>Velázquez Aguilar, V. M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Effects of the free evolution in the Arthurs–Kelly model of simultaneous measurement and in the retrodictive predictions of the Heisenberg uncertainty relations</atitle><jtitle>European physical journal plus</jtitle><stitle>Eur. Phys. J. Plus</stitle><date>2021-09-01</date><risdate>2021</risdate><volume>136</volume><issue>9</issue><spage>954</spage><pages>954-</pages><artnum>954</artnum><issn>2190-5444</issn><eissn>2190-5444</eissn><abstract>Since its conception, the simultaneous measurement approach of Arthurs and Kelly has been a significant tool for the better understanding of the measurement process in quantum mechanics. This model considers a strong interaction Hamiltonian by discarding the free evolution part. In this work, we study the effect of the full dynamics—taking into account the free Hamiltonian—on the optimal limits of retrodictive and predictive accuracy of the simultaneous measurement process of position and momentum observables. To do that, we consider a minimum uncertainty Gaussian state as the system under inspection, which allows to carry out an optimal simultaneous measurement. We show that the inclusion of the free Hamiltonian induces a spreading on the probability density of the measurement setting, which increases the value of the product of the variances of the so-called retrodictive and predictive error operators, this is equivalent to a reduction in the accuracy of the measurement.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1140/epjp/s13360-021-01943-6</doi><orcidid>https://orcid.org/0000-0001-7603-3667</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 2190-5444 |
| ispartof | European physical journal plus, 2021-09, Vol.136 (9), p.954, Article 954 |
| issn | 2190-5444 2190-5444 |
| language | eng |
| recordid | cdi_proquest_journals_2919501840 |
| source | AUTh Library subscriptions: ProQuest Central; Springer Journals |
| subjects | Accuracy Applied and Technical Physics Atomic Commuting Complex Systems Condensed Matter Physics Evolution Hamiltonian functions Mathematical and Computational Physics Measurement techniques Molecular Optical and Plasma Physics Physics Physics and Astronomy Position measurement Probability Quantum mechanics Quantum physics Regular Article Standard deviation Theoretical Uncertainty |
| title | Effects of the free evolution in the Arthurs–Kelly model of simultaneous measurement and in the retrodictive predictions of the Heisenberg uncertainty relations |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-14T17%3A22%3A44IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Effects%20of%20the%20free%20evolution%20in%20the%20Arthurs%E2%80%93Kelly%20model%20of%20simultaneous%20measurement%20and%20in%20the%20retrodictive%20predictions%20of%20the%20Heisenberg%20uncertainty%20relations&rft.jtitle=European%20physical%20journal%20plus&rft.au=Mendoza-Fierro,%20J.%20A.&rft.date=2021-09-01&rft.volume=136&rft.issue=9&rft.spage=954&rft.pages=954-&rft.artnum=954&rft.issn=2190-5444&rft.eissn=2190-5444&rft_id=info:doi/10.1140/epjp/s13360-021-01943-6&rft_dat=%3Cproquest_cross%3E2919501840%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2919501840&rft_id=info:pmid/&rfr_iscdi=true |