Entropic Energy-Time Uncertainty Relation
Energy-time uncertainty plays an important role in quantum foundations and technologies, and it was even discussed by the founders of quantum mechanics. However, standard approaches (e.g., Robertson’s uncertainty relation) do not apply to energy-time uncertainty because, in general, there is no Herm...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2019
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| Online Access: | http://hdl.handle.net/1721.1/120976 |
| _version_ | 1811093323415289856 |
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| author | Coles, Patrick J. Katariya, Vishal Lloyd, Seth Marvian, Iman Wilde, Mark M. |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Coles, Patrick J. Katariya, Vishal Lloyd, Seth Marvian, Iman Wilde, Mark M. |
| author_sort | Coles, Patrick J. |
| collection | MIT |
| description | Energy-time uncertainty plays an important role in quantum foundations and technologies, and it was even discussed by the founders of quantum mechanics. However, standard approaches (e.g., Robertson’s uncertainty relation) do not apply to energy-time uncertainty because, in general, there is no Hermitian operator associated with time. Following previous approaches, we quantify time uncertainty by how well one can read off the time from a quantum clock. We then use entropy to quantify the information-theoretic distinguishability of the various time states of the clock. Our main result is an entropic energy-time uncertainty relation for general time-independent Hamiltonians, stated for both the discrete-time and continuous-time cases. Our uncertainty relation is strong, in the sense that it allows for a quantum memory to help reduce the uncertainty, and this formulation leads us to reinterpret it as a bound on the relative entropy of asymmetry. Because of the operational relevance of entropy, we anticipate that our uncertainty relation will have information-processing applications. |
| first_indexed | 2024-09-23T15:43:26Z |
| format | Article |
| id | mit-1721.1/120976 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T15:43:26Z |
| publishDate | 2019 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1209762022-10-02T03:41:00Z Entropic Energy-Time Uncertainty Relation Coles, Patrick J. Katariya, Vishal Lloyd, Seth Marvian, Iman Wilde, Mark M. Massachusetts Institute of Technology. Department of Mechanical Engineering Massachusetts Institute of Technology. Research Laboratory of Electronics Lloyd, Seth Energy-time uncertainty plays an important role in quantum foundations and technologies, and it was even discussed by the founders of quantum mechanics. However, standard approaches (e.g., Robertson’s uncertainty relation) do not apply to energy-time uncertainty because, in general, there is no Hermitian operator associated with time. Following previous approaches, we quantify time uncertainty by how well one can read off the time from a quantum clock. We then use entropy to quantify the information-theoretic distinguishability of the various time states of the clock. Our main result is an entropic energy-time uncertainty relation for general time-independent Hamiltonians, stated for both the discrete-time and continuous-time cases. Our uncertainty relation is strong, in the sense that it allows for a quantum memory to help reduce the uncertainty, and this formulation leads us to reinterpret it as a bound on the relative entropy of asymmetry. Because of the operational relevance of entropy, we anticipate that our uncertainty relation will have information-processing applications. 2019-03-15T12:53:33Z 2019-03-15T12:53:33Z 2019-03 2018-06 2019-03-13T18:00:18Z Article http://purl.org/eprint/type/JournalArticle 0031-9007 1079-7114 http://hdl.handle.net/1721.1/120976 Coles, Patrick J. et al. "Entropic Energy-Time Uncertainty Relation." Physical Review Letters 122, 10 (March 2019): 100401 © 2019 American Physical Society en http://dx.doi.org/10.1103/PhysRevLett.122.100401 Physical Review Letters Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Coles, Patrick J. Katariya, Vishal Lloyd, Seth Marvian, Iman Wilde, Mark M. Entropic Energy-Time Uncertainty Relation |
| title | Entropic Energy-Time Uncertainty Relation |
| title_full | Entropic Energy-Time Uncertainty Relation |
| title_fullStr | Entropic Energy-Time Uncertainty Relation |
| title_full_unstemmed | Entropic Energy-Time Uncertainty Relation |
| title_short | Entropic Energy-Time Uncertainty Relation |
| title_sort | entropic energy time uncertainty relation |
| url | http://hdl.handle.net/1721.1/120976 |
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