Majorization preservation of Gaussian bosonic channels
It is shown that phase-insensitive Gaussian bosonic channels are majorization-preserving over the set of passive states of the harmonic oscillator. This means that comparable passive states under majorization are transformed into equally comparable passive states by any phase-insensitive Gaussian bo...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2016-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/18/7/073047 |
| _version_ | 1797750941114433536 |
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| author | Michael G Jabbour Raúl García-Patrón Nicolas J Cerf |
| author_facet | Michael G Jabbour Raúl García-Patrón Nicolas J Cerf |
| author_sort | Michael G Jabbour |
| collection | DOAJ |
| description | It is shown that phase-insensitive Gaussian bosonic channels are majorization-preserving over the set of passive states of the harmonic oscillator. This means that comparable passive states under majorization are transformed into equally comparable passive states by any phase-insensitive Gaussian bosonic channel. Our proof relies on a new preorder relation called Fock-majorization, which coincides with regular majorization for passive states but also induces another order relation in terms of mean boson number, thereby connecting the concepts of energy and disorder of a quantum state. The consequences of majorization preservation are discussed in the context of the broadcast communication capacity of Gaussian bosonic channels. Because most of our results are independent of the specific nature of the system under investigation, they could be generalized to other quantum systems and Hamiltonians, providing a new tool that may prove useful in quantum information theory and especially quantum thermodynamics. |
| first_indexed | 2024-03-12T16:41:06Z |
| format | Article |
| id | doaj.art-04e5b963fc194e38947dc81dee0f5a28 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:41:06Z |
| publishDate | 2016-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-04e5b963fc194e38947dc81dee0f5a282023-08-08T14:29:38ZengIOP PublishingNew Journal of Physics1367-26302016-01-0118707304710.1088/1367-2630/18/7/073047Majorization preservation of Gaussian bosonic channelsMichael G Jabbour0Raúl García-Patrón1Nicolas J Cerf2Quantum Information and Communication, École polytechnique de Bruxelles, CP 165, Université libre de Bruxelles , 1050 Bruxelles, BelgiumQuantum Information and Communication, École polytechnique de Bruxelles, CP 165, Université libre de Bruxelles , 1050 Bruxelles, BelgiumQuantum Information and Communication, École polytechnique de Bruxelles, CP 165, Université libre de Bruxelles , 1050 Bruxelles, BelgiumIt is shown that phase-insensitive Gaussian bosonic channels are majorization-preserving over the set of passive states of the harmonic oscillator. This means that comparable passive states under majorization are transformed into equally comparable passive states by any phase-insensitive Gaussian bosonic channel. Our proof relies on a new preorder relation called Fock-majorization, which coincides with regular majorization for passive states but also induces another order relation in terms of mean boson number, thereby connecting the concepts of energy and disorder of a quantum state. The consequences of majorization preservation are discussed in the context of the broadcast communication capacity of Gaussian bosonic channels. Because most of our results are independent of the specific nature of the system under investigation, they could be generalized to other quantum systems and Hamiltonians, providing a new tool that may prove useful in quantum information theory and especially quantum thermodynamics.https://doi.org/10.1088/1367-2630/18/7/073047quantum channelsquantum opticsgaussian bosonic channelsmajorization theorypassive states |
| spellingShingle | Michael G Jabbour Raúl García-Patrón Nicolas J Cerf Majorization preservation of Gaussian bosonic channels New Journal of Physics quantum channels quantum optics gaussian bosonic channels majorization theory passive states |
| title | Majorization preservation of Gaussian bosonic channels |
| title_full | Majorization preservation of Gaussian bosonic channels |
| title_fullStr | Majorization preservation of Gaussian bosonic channels |
| title_full_unstemmed | Majorization preservation of Gaussian bosonic channels |
| title_short | Majorization preservation of Gaussian bosonic channels |
| title_sort | majorization preservation of gaussian bosonic channels |
| topic | quantum channels quantum optics gaussian bosonic channels majorization theory passive states |
| url | https://doi.org/10.1088/1367-2630/18/7/073047 |
| work_keys_str_mv | AT michaelgjabbour majorizationpreservationofgaussianbosonicchannels AT raulgarciapatron majorizationpreservationofgaussianbosonicchannels AT nicolasjcerf majorizationpreservationofgaussianbosonicchannels |