Resource theory of non-Gaussian operations
Non-Gaussian states and operations are crucial for various continuous-variable quantum information processing tasks. To quantitatively understand non-Gaussianity beyond states, we establish a resource theory for non-Gaussian operations. In our framework, we consider Gaussian operations as free opera...
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| Format: | Article |
| Language: | English |
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American Physical Society
2018
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| Online Access: | http://hdl.handle.net/1721.1/115532 https://orcid.org/0000-0002-9554-3846 https://orcid.org/0000-0003-4626-5648 https://orcid.org/0000-0002-6094-5861 |
| _version_ | 1826204377506906112 |
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| author | Zhuang, Quntao Shor, Peter Williston Shapiro, Jeffrey H |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Zhuang, Quntao Shor, Peter Williston Shapiro, Jeffrey H |
| author_sort | Zhuang, Quntao |
| collection | MIT |
| description | Non-Gaussian states and operations are crucial for various continuous-variable quantum information processing tasks. To quantitatively understand non-Gaussianity beyond states, we establish a resource theory for non-Gaussian operations. In our framework, we consider Gaussian operations as free operations, and non-Gaussian operations as resources. We define entanglement-assisted non-Gaussianity generating power and show that it is a monotone that is nonincreasing under the set of free superoperations, i.e., concatenation and tensoring with Gaussian channels. For conditional unitary maps, this monotone can be analytically calculated. As examples, we show that the non-Gaussianity of ideal photon-number subtraction and photon-number addition equal the non-Gaussianity of the single-photon Fock state. Based on our non-Gaussianity monotone, we divide non-Gaussian operations into two classes: (i) the finite non-Gaussianity class, e.g., photon-number subtraction, photon-number addition, and all Gaussian-dilatable non-Gaussian channels; and (ii) the diverging non-Gaussianity class, e.g., the binary phase-shift channel and the Kerr nonlinearity. This classification also implies that not all non-Gaussian channels are exactly Gaussian dilatable. Our resource theory enables a quantitative characterization and a first classification of non-Gaussian operations, paving the way towards the full understanding of non-Gaussianity. |
| first_indexed | 2024-09-23T12:53:45Z |
| format | Article |
| id | mit-1721.1/115532 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T12:53:45Z |
| publishDate | 2018 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1155322022-09-28T10:47:06Z Resource theory of non-Gaussian operations Zhuang, Quntao Shor, Peter Williston Shapiro, Jeffrey H Massachusetts Institute of Technology. Center for Theoretical Physics Massachusetts Institute of Technology. Department of Mathematics Massachusetts Institute of Technology. Department of Physics Massachusetts Institute of Technology. Research Laboratory of Electronics Zhuang, Quntao Shor, Peter Williston Shapiro, Jeffrey H Non-Gaussian states and operations are crucial for various continuous-variable quantum information processing tasks. To quantitatively understand non-Gaussianity beyond states, we establish a resource theory for non-Gaussian operations. In our framework, we consider Gaussian operations as free operations, and non-Gaussian operations as resources. We define entanglement-assisted non-Gaussianity generating power and show that it is a monotone that is nonincreasing under the set of free superoperations, i.e., concatenation and tensoring with Gaussian channels. For conditional unitary maps, this monotone can be analytically calculated. As examples, we show that the non-Gaussianity of ideal photon-number subtraction and photon-number addition equal the non-Gaussianity of the single-photon Fock state. Based on our non-Gaussianity monotone, we divide non-Gaussian operations into two classes: (i) the finite non-Gaussianity class, e.g., photon-number subtraction, photon-number addition, and all Gaussian-dilatable non-Gaussian channels; and (ii) the diverging non-Gaussianity class, e.g., the binary phase-shift channel and the Kerr nonlinearity. This classification also implies that not all non-Gaussian channels are exactly Gaussian dilatable. Our resource theory enables a quantitative characterization and a first classification of non-Gaussian operations, paving the way towards the full understanding of non-Gaussianity. United States. Air Force. Office of Scientific Research (Grant FA9550-14-1-0052) National Science Foundation (U.S.) (Grant CCF-1525130) National Science Foundation (U.S.) (Grant CCF0-939370) 2018-05-21T14:15:25Z 2018-05-21T14:15:25Z 2018-05 2018-03 2018-05-14T18:00:24Z Article http://purl.org/eprint/type/JournalArticle 2469-9926 2469-9934 http://hdl.handle.net/1721.1/115532 Zhuang, Quntao et al. "Resource theory of non-Gaussian operations." Physical Review A 97, 5 (May 2018): 052317 © 2018 American Physical Society https://orcid.org/0000-0002-9554-3846 https://orcid.org/0000-0003-4626-5648 https://orcid.org/0000-0002-6094-5861 en http://dx.doi.org/10.1103/PhysRevA.97.052317 Physical Review A 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 | Zhuang, Quntao Shor, Peter Williston Shapiro, Jeffrey H Resource theory of non-Gaussian operations |
| title | Resource theory of non-Gaussian operations |
| title_full | Resource theory of non-Gaussian operations |
| title_fullStr | Resource theory of non-Gaussian operations |
| title_full_unstemmed | Resource theory of non-Gaussian operations |
| title_short | Resource theory of non-Gaussian operations |
| title_sort | resource theory of non gaussian operations |
| url | http://hdl.handle.net/1721.1/115532 https://orcid.org/0000-0002-9554-3846 https://orcid.org/0000-0003-4626-5648 https://orcid.org/0000-0002-6094-5861 |
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