A framework for phase and interference in generalized probabilistic theories
Phase plays a crucial role in many quantum effects including interference. Here we lay the foundations for the study of phase in probabilistic theories more generally. Phase is normally defined in terms of complex numbers that appear when representing quantum states as complex vectors. Here we give...
| Glavni autori: | , , , , |
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| Format: | Journal article |
| Jezik: | English |
| Izdano: |
2013
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| _version_ | 1826290158156120064 |
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| author | Garner, A Dahlsten, O Nakata, Y Murao, M Vedral, V |
| author_facet | Garner, A Dahlsten, O Nakata, Y Murao, M Vedral, V |
| author_sort | Garner, A |
| collection | OXFORD |
| description | Phase plays a crucial role in many quantum effects including interference. Here we lay the foundations for the study of phase in probabilistic theories more generally. Phase is normally defined in terms of complex numbers that appear when representing quantum states as complex vectors. Here we give an operational definition whereby phase is instead defined in terms of measurement statistics. Our definition is phrased in terms of the operational framework known as generalized probabilistic theories or the convex framework. The definition makes it possible to ask whether other theories in this framework can also have phase. We apply our definition to investigate phase and interference in several example theories: classical probability theory, a version of Spekkens' toy model, quantum theory and box-world. We find that phase is ubiquitous; any non-classical theory can be said to have non-trivial phase dynamics. © IOP Publishing and Deutsche Physikalische Gesellschaft. |
| first_indexed | 2024-03-07T02:39:54Z |
| format | Journal article |
| id | oxford-uuid:aa11ef9a-9959-4648-ae71-b1534c7196bc |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:39:54Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | oxford-uuid:aa11ef9a-9959-4648-ae71-b1534c7196bc2022-03-27T03:12:49ZA framework for phase and interference in generalized probabilistic theoriesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:aa11ef9a-9959-4648-ae71-b1534c7196bcEnglishSymplectic Elements at Oxford2013Garner, ADahlsten, ONakata, YMurao, MVedral, VPhase plays a crucial role in many quantum effects including interference. Here we lay the foundations for the study of phase in probabilistic theories more generally. Phase is normally defined in terms of complex numbers that appear when representing quantum states as complex vectors. Here we give an operational definition whereby phase is instead defined in terms of measurement statistics. Our definition is phrased in terms of the operational framework known as generalized probabilistic theories or the convex framework. The definition makes it possible to ask whether other theories in this framework can also have phase. We apply our definition to investigate phase and interference in several example theories: classical probability theory, a version of Spekkens' toy model, quantum theory and box-world. We find that phase is ubiquitous; any non-classical theory can be said to have non-trivial phase dynamics. © IOP Publishing and Deutsche Physikalische Gesellschaft. |
| spellingShingle | Garner, A Dahlsten, O Nakata, Y Murao, M Vedral, V A framework for phase and interference in generalized probabilistic theories |
| title | A framework for phase and interference in generalized probabilistic theories |
| title_full | A framework for phase and interference in generalized probabilistic theories |
| title_fullStr | A framework for phase and interference in generalized probabilistic theories |
| title_full_unstemmed | A framework for phase and interference in generalized probabilistic theories |
| title_short | A framework for phase and interference in generalized probabilistic theories |
| title_sort | framework for phase and interference in generalized probabilistic theories |
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