The One-Mode Quantum-Limited Gaussian Attenuator and Amplifier Have Gaussian Maximizers

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Standard

The One-Mode Quantum-Limited Gaussian Attenuator and Amplifier Have Gaussian Maximizers. / De Palma, Giacomo; Trevisan, Dario; Giovannetti, Vittorio.

In: Annales Henri Poincare, Vol. 19, No. 10, 2018, p. 2919-2953.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

De Palma, G, Trevisan, D & Giovannetti, V 2018, 'The One-Mode Quantum-Limited Gaussian Attenuator and Amplifier Have Gaussian Maximizers', Annales Henri Poincare, vol. 19, no. 10, pp. 2919-2953. https://doi.org/10.1007/s00023-018-0703-5

APA

De Palma, G., Trevisan, D., & Giovannetti, V. (2018). The One-Mode Quantum-Limited Gaussian Attenuator and Amplifier Have Gaussian Maximizers. Annales Henri Poincare, 19(10), 2919-2953. https://doi.org/10.1007/s00023-018-0703-5

Vancouver

De Palma G, Trevisan D, Giovannetti V. The One-Mode Quantum-Limited Gaussian Attenuator and Amplifier Have Gaussian Maximizers. Annales Henri Poincare. 2018;19(10):2919-2953. https://doi.org/10.1007/s00023-018-0703-5

Author

De Palma, Giacomo ; Trevisan, Dario ; Giovannetti, Vittorio. / The One-Mode Quantum-Limited Gaussian Attenuator and Amplifier Have Gaussian Maximizers. In: Annales Henri Poincare. 2018 ; Vol. 19, No. 10. pp. 2919-2953.

Bibtex

@article{963261095fd243a2acbdb8d6a9177295,
title = "The One-Mode Quantum-Limited Gaussian Attenuator and Amplifier Have Gaussian Maximizers",
abstract = "We determine the p. q norms of the Gaussian one-mode quantum-limited attenuator and amplifier and prove that they are achieved by Gaussian states, extending to noncommutative probability the seminal theorem {"} Gaussian kernels have only Gaussian maximizers{"} (Lieb in Invent Math 102(1): 179-208, 1990). The quantum-limited attenuator and amplifier are the building blocks of quantum Gaussian channels, which play a key role in quantum communication theory since they model in the quantum regime the attenuation and the noise affecting any electromagnetic signal. Our result is crucial to prove the longstanding conjecture stating that Gaussian input states minimize the output entropy of one-mode phase-covariant quantum Gaussian channels for fixed input entropy. Our proof technique is based on a new noncommutative logarithmic Sobolev inequality, and it can be used to determine the p. q norms of any quantum semigroup.",
author = "{De Palma}, Giacomo and Dario Trevisan and Vittorio Giovannetti",
year = "2018",
doi = "10.1007/s00023-018-0703-5",
language = "English",
volume = "19",
pages = "2919--2953",
journal = "Annales Henri Poincare",
issn = "1424-0637",
publisher = "Springer Basel AG",
number = "10",

}

RIS

TY - JOUR

T1 - The One-Mode Quantum-Limited Gaussian Attenuator and Amplifier Have Gaussian Maximizers

AU - De Palma, Giacomo

AU - Trevisan, Dario

AU - Giovannetti, Vittorio

PY - 2018

Y1 - 2018

N2 - We determine the p. q norms of the Gaussian one-mode quantum-limited attenuator and amplifier and prove that they are achieved by Gaussian states, extending to noncommutative probability the seminal theorem " Gaussian kernels have only Gaussian maximizers" (Lieb in Invent Math 102(1): 179-208, 1990). The quantum-limited attenuator and amplifier are the building blocks of quantum Gaussian channels, which play a key role in quantum communication theory since they model in the quantum regime the attenuation and the noise affecting any electromagnetic signal. Our result is crucial to prove the longstanding conjecture stating that Gaussian input states minimize the output entropy of one-mode phase-covariant quantum Gaussian channels for fixed input entropy. Our proof technique is based on a new noncommutative logarithmic Sobolev inequality, and it can be used to determine the p. q norms of any quantum semigroup.

AB - We determine the p. q norms of the Gaussian one-mode quantum-limited attenuator and amplifier and prove that they are achieved by Gaussian states, extending to noncommutative probability the seminal theorem " Gaussian kernels have only Gaussian maximizers" (Lieb in Invent Math 102(1): 179-208, 1990). The quantum-limited attenuator and amplifier are the building blocks of quantum Gaussian channels, which play a key role in quantum communication theory since they model in the quantum regime the attenuation and the noise affecting any electromagnetic signal. Our result is crucial to prove the longstanding conjecture stating that Gaussian input states minimize the output entropy of one-mode phase-covariant quantum Gaussian channels for fixed input entropy. Our proof technique is based on a new noncommutative logarithmic Sobolev inequality, and it can be used to determine the p. q norms of any quantum semigroup.

U2 - 10.1007/s00023-018-0703-5

DO - 10.1007/s00023-018-0703-5

M3 - Journal article

VL - 19

SP - 2919

EP - 2953

JO - Annales Henri Poincare

JF - Annales Henri Poincare

SN - 1424-0637

IS - 10

ER -

ID: 203245460