Resource theory of non-Gaussian operations
Non-Gaussian states and operations are crucial for various continuous-variable quantum information processingtasks. To quantitatively understand non-Gaussianity beyond states, we establish a resource theory for non-Gaussianoperations. In our framework, we consider Gaussian operations as free operati...
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2020
|
| Online Access: | https://hdl.handle.net/1721.1/126684 |
| _version_ | 1826207906413936640 |
|---|---|
| author | Zhuang, Quntao Shor, Peter Williston Shapiro, Jeffrey H |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of 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 processingtasks. To quantitatively understand non-Gaussianity beyond states, we establish a resource theory for non-Gaussianoperations. In our framework, we consider Gaussian operations as free operations, and non-Gaussian operationsas resources. We define entanglement-assisted non-Gaussianity generating power and show that it is a monotonethat is nonincreasing under the set of free superoperations, i.e., concatenation and tensoring with Gaussianchannels. For conditional unitary maps, this monotone can be analytically calculated. As examples, we show thatthe non-Gaussianity of ideal photon-number subtraction and photon-number addition equal the non-Gaussianityof the single-photon Fock state. Based on our non-Gaussianity monotone, we divide non-Gaussian operationsinto 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 binaryphase-shift channel and the Kerr nonlinearity. This classification also implies that not all non-Gaussian channelsare exactly Gaussian dilatable. Our resource theory enables a quantitative characterization and a first classificationof non-Gaussian operations, paving the way towards the full understanding of non-Gaussianity. |
| first_indexed | 2024-09-23T13:56:49Z |
| format | Article |
| id | mit-1721.1/126684 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T13:56:49Z |
| publishDate | 2020 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1266842022-09-28T17:19:38Z Resource theory of non-Gaussian operations Zhuang, Quntao Shor, Peter Williston Shapiro, Jeffrey H Massachusetts Institute of Technology. Department of Physics Massachusetts Institute of Technology. Research Laboratory of Electronics Massachusetts Institute of Technology. Center for Theoretical Physics Massachusetts Institute of Technology. Department of Mathematics Non-Gaussian states and operations are crucial for various continuous-variable quantum information processingtasks. To quantitatively understand non-Gaussianity beyond states, we establish a resource theory for non-Gaussianoperations. In our framework, we consider Gaussian operations as free operations, and non-Gaussian operationsas resources. We define entanglement-assisted non-Gaussianity generating power and show that it is a monotonethat is nonincreasing under the set of free superoperations, i.e., concatenation and tensoring with Gaussianchannels. For conditional unitary maps, this monotone can be analytically calculated. As examples, we show thatthe non-Gaussianity of ideal photon-number subtraction and photon-number addition equal the non-Gaussianityof the single-photon Fock state. Based on our non-Gaussianity monotone, we divide non-Gaussian operationsinto 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 binaryphase-shift channel and the Kerr nonlinearity. This classification also implies that not all non-Gaussian channelsare exactly Gaussian dilatable. Our resource theory enables a quantitative characterization and a first classificationof non-Gaussian operations, paving the way towards the full understanding of non-Gaussianity. 2020-08-19T19:53:06Z 2020-08-19T19:53:06Z 2018-05 2018-03 2019-11-20T13:48:19Z Article http://purl.org/eprint/type/JournalArticle 2469-9934 2469-9926 https://hdl.handle.net/1721.1/126684 Zhuang, Quntao, Peter W. Shor and Jeffrey H. Shapiro. “Resource theory of non-Gaussian operations.” Physical review. A, vol. 97, 2018, article 052317 © 2018 The Author(s) en 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. application/pdf American Physical Society APS |
| 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 | https://hdl.handle.net/1721.1/126684 |
| work_keys_str_mv | AT zhuangquntao resourcetheoryofnongaussianoperations AT shorpeterwilliston resourcetheoryofnongaussianoperations AT shapirojeffreyh resourcetheoryofnongaussianoperations |