Quantum correlations which imply causation
In ordinary, non-relativistic, quantum physics, time enters only as a parameter and not as an observable [1]: a state of a physical system is specified at a given time and then evolved according to the prescribed dynamics. While the state can, and usually does, extend across all space, it is only de...
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| Format: | Journal article |
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Nature Publishing Group
2015
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| _version_ | 1826285418474110976 |
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| author | Jones, J Vedral, V Fitzsimons, J |
| author_facet | Jones, J Vedral, V Fitzsimons, J |
| author_sort | Jones, J |
| collection | OXFORD |
| description | In ordinary, non-relativistic, quantum physics, time enters only as a parameter and not as an observable [1]: a state of a physical system is specified at a given time and then evolved according to the prescribed dynamics. While the state can, and usually does, extend across all space, it is only defined at one instant of time. Here we ask what would happen if we defined the notion of the quantum density matrix for multiple spatial and temporal measurements. We introduce the concept of a pseudo-density matrix (PDM) which treats space and time indiscriminately. This matrix in general fails to be positive for measurement events which do not occur simultaneously, motivating us to define a measure of causality that discriminates between spatial and temporal correlations. Important properties of this measure, such as monotonicity under local operations, are proved. Two qubit NMR experiments are presented that illustrate how a temporal pseudo-density matrix approaches a genuinely allowed density matrix as the amount of decoherence is increased between two consecutive measurements. |
| first_indexed | 2024-03-07T01:28:32Z |
| format | Journal article |
| id | oxford-uuid:92cb2d7b-99fb-43ce-8613-795860758965 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T01:28:32Z |
| publishDate | 2015 |
| publisher | Nature Publishing Group |
| record_format | dspace |
| spelling | oxford-uuid:92cb2d7b-99fb-43ce-8613-7958607589652022-03-26T23:28:01ZQuantum correlations which imply causationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:92cb2d7b-99fb-43ce-8613-795860758965Symplectic Elements at OxfordNature Publishing Group2015Jones, JVedral, VFitzsimons, JIn ordinary, non-relativistic, quantum physics, time enters only as a parameter and not as an observable [1]: a state of a physical system is specified at a given time and then evolved according to the prescribed dynamics. While the state can, and usually does, extend across all space, it is only defined at one instant of time. Here we ask what would happen if we defined the notion of the quantum density matrix for multiple spatial and temporal measurements. We introduce the concept of a pseudo-density matrix (PDM) which treats space and time indiscriminately. This matrix in general fails to be positive for measurement events which do not occur simultaneously, motivating us to define a measure of causality that discriminates between spatial and temporal correlations. Important properties of this measure, such as monotonicity under local operations, are proved. Two qubit NMR experiments are presented that illustrate how a temporal pseudo-density matrix approaches a genuinely allowed density matrix as the amount of decoherence is increased between two consecutive measurements. |
| spellingShingle | Jones, J Vedral, V Fitzsimons, J Quantum correlations which imply causation |
| title | Quantum correlations which imply causation |
| title_full | Quantum correlations which imply causation |
| title_fullStr | Quantum correlations which imply causation |
| title_full_unstemmed | Quantum correlations which imply causation |
| title_short | Quantum correlations which imply causation |
| title_sort | quantum correlations which imply causation |
| work_keys_str_mv | AT jonesj quantumcorrelationswhichimplycausation AT vedralv quantumcorrelationswhichimplycausation AT fitzsimonsj quantumcorrelationswhichimplycausation |