Passive states as optimal inputs for single-jump lossy quantum channels
The passive states of a quantum system minimize the average energy among all the states with a given spectrum. We prove that passive states are the optimal inputs of single-jump lossy quantum channels. These channels arise from a weak interaction of the quantum system of interest with a large Markov...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2017
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| Online Access: | http://hdl.handle.net/1721.1/110603 |
| _version_ | 1826210233253363712 |
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| author | De Palma, Giacomo Mari, Andrea Lloyd, Seth Giovannetti, Vittorio |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering De Palma, Giacomo Mari, Andrea Lloyd, Seth Giovannetti, Vittorio |
| author_sort | De Palma, Giacomo |
| collection | MIT |
| description | The passive states of a quantum system minimize the average energy among all the states with a given spectrum. We prove that passive states are the optimal inputs of single-jump lossy quantum channels. These channels arise from a weak interaction of the quantum system of interest with a large Markovian bath in its ground state, such that the interaction Hamiltonian couples only consecutive energy eigenstates of the system. We prove that the output generated by any input state ρ majorizes the output generated by the passive input state ρ[subscript 0] with the same spectrum of ρ. Then, the output generated by ρ can be obtained applying a random unitary operation to the output generated by ρ[superscript 0]. This is an extension of De Palma et al. [IEEE Trans. Inf. Theory 62, 2895 (2016)], where the same result is proved for one-mode bosonic Gaussian channels. We also prove that for finite temperature this optimality property can fail already in a two-level system, where the best input is a coherent superposition of the two energy eigenstates. |
| first_indexed | 2024-09-23T14:46:34Z |
| format | Article |
| id | mit-1721.1/110603 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T14:46:34Z |
| publishDate | 2017 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1106032022-10-01T22:23:46Z Passive states as optimal inputs for single-jump lossy quantum channels De Palma, Giacomo Mari, Andrea Lloyd, Seth Giovannetti, Vittorio Massachusetts Institute of Technology. Department of Mechanical Engineering Massachusetts Institute of Technology. Research Laboratory of Electronics Lloyd, Seth The passive states of a quantum system minimize the average energy among all the states with a given spectrum. We prove that passive states are the optimal inputs of single-jump lossy quantum channels. These channels arise from a weak interaction of the quantum system of interest with a large Markovian bath in its ground state, such that the interaction Hamiltonian couples only consecutive energy eigenstates of the system. We prove that the output generated by any input state ρ majorizes the output generated by the passive input state ρ[subscript 0] with the same spectrum of ρ. Then, the output generated by ρ can be obtained applying a random unitary operation to the output generated by ρ[superscript 0]. This is an extension of De Palma et al. [IEEE Trans. Inf. Theory 62, 2895 (2016)], where the same result is proved for one-mode bosonic Gaussian channels. We also prove that for finite temperature this optimality property can fail already in a two-level system, where the best input is a coherent superposition of the two energy eigenstates. 2017-07-10T19:12:08Z 2017-07-10T19:12:08Z 2016-06 2016-03 2016-06-21T22:00:06Z Article http://purl.org/eprint/type/JournalArticle 2469-9926 2469-9934 http://hdl.handle.net/1721.1/110603 De Palma, Giacomo et al. “Passive States as Optimal Inputs for Single-Jump Lossy Quantum Channels.” Physical Review A 93.6 (2016): n. pag. © 2016 American Physical Society en http://dx.doi.org/10.1103/PhysRevA.93.062328 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 | De Palma, Giacomo Mari, Andrea Lloyd, Seth Giovannetti, Vittorio Passive states as optimal inputs for single-jump lossy quantum channels |
| title | Passive states as optimal inputs for single-jump lossy quantum channels |
| title_full | Passive states as optimal inputs for single-jump lossy quantum channels |
| title_fullStr | Passive states as optimal inputs for single-jump lossy quantum channels |
| title_full_unstemmed | Passive states as optimal inputs for single-jump lossy quantum channels |
| title_short | Passive states as optimal inputs for single-jump lossy quantum channels |
| title_sort | passive states as optimal inputs for single jump lossy quantum channels |
| url | http://hdl.handle.net/1721.1/110603 |
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