Entanglement and squeezing in continuous-variable systems

Manuel Gessner; Luca Pezzè; Augusto Smerzi

doi:10.22331/q-2017-07-14-17

Entanglement and squeezing in continuous-variable systems

Manuel Gessner, Luca Pezzè, and Augusto Smerzi

QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, I-50125 Firenze, Italy

Published:	2017-07-14, volume 1, page 17
Eprint:	arXiv:1702.08413v3
Doi:	https://doi.org/10.22331/q-2017-07-14-17
Citation:	Quantum 1, 17 (2017).

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Abstract

We introduce a multi-mode squeezing coefficient to characterize entanglement in $N$-partite continuous-variable systems. The coefficient relates to the squeezing of collective observables in the $2N$-dimensional phase space and can be readily extracted from the covariance matrix. Simple extensions further permit to reveal entanglement within specific partitions of a multipartite system. Applications with nonlinear observables allow for the detection of non-Gaussian entanglement.

Popular summary

Quantum mechanical squeezing shrinks the variance of one observable at the expense of another, and can thereby reduce the quantum noise in a measurement. In collective spin systems, it is possible to quantify the degree of squeezing and relate it to entanglement using spin-squeezing coefficients. Similar tools have so far been unavailable for continuous-variable systems, due to the unbounded Hilbert space. In this article, we introduce a bosonic squeezing coefficient that identifies multimode continuous-variable squeezing. Using this coefficient, we can show that multimode squeezing indeed implies mode entanglement. The coefficient can be obtained directly from the covariance matrix, which is accessible in many experiments.

► BibTeX data

@article{Gessner2017entanglement,
  doi = {10.22331/q-2017-07-14-17},
  url = {https://doi.org/10.22331/q-2017-07-14-17},
  title = {Entanglement and squeezing in continuous-variable systems},
  author = {Gessner, Manuel and Pezz{\`{e}}, Luca and Smerzi, Augusto},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {1},
  pages = {17},
  month = jul,
  year = {2017}
}

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[1] Manuel Gessner, Augusto Smerzi, and Luca Pezzè, "Metrological Nonlinear Squeezing Parameter", Physical Review Letters 122 9, 090503 (2019).

[2] Philipp Kunkel, Maximilian Prüfer, Helmut Strobel, Daniel Linnemann, Anika Frölian, Thomas Gasenzer, Martin Gärttner, and Markus K. Oberthaler, "Spatially distributed multipartite entanglement enables EPR steering of atomic clouds", Science 360 6387, 413 (2018).

[3] Matteo Fadel, Quantum Science and Technology 57 (2021) ISBN:978-3-030-85471-3.

[4] Mattia Walschaers, "Non-Gaussian Quantum States and Where to Find Them", PRX Quantum 2 3, 030204 (2021).

[5] Matteo Fadel and Manuel Gessner, "Entanglement of Local Hidden States", Quantum 6, 651 (2022).

[6] Manuel Gessner, Luca Pezzè, and Augusto Smerzi, "Sensitivity Bounds for Multiparameter Quantum Metrology", Physical Review Letters 121 13, 130503 (2018).

[7] Matteo Fadel and Manuel Gessner, "Relating spin squeezing to multipartite entanglement criteria for particles and modes", Physical Review A 102 1, 012412 (2020).

[8] Manuel Gessner, Augusto Smerzi, and Luca Pezzè, "Multiparameter squeezing for optimal quantum enhancements in sensor networks", Nature Communications 11 1, 3817 (2020).

[9] Zhongzhong Qin, Manuel Gessner, Zhihong Ren, Xiaowei Deng, Dongmei Han, Weidong Li, Xiaolong Su, Augusto Smerzi, and Kunchi Peng, "Characterizing the multipartite continuous-variable entanglement structure from squeezing coefficients and the Fisher information", npj Quantum Information 5 1, 3 (2019).

[10] Zhi-Hong Ren, Yan Li, Yan-Na Li, and Wei-Dong Li, "Development on quantum metrology with quantum Fisher information", Acta Physica Sinica 68 4, 040601 (2019).

[11] Manuel Gessner and Augusto Smerzi, "Statistical speed of quantum states: Generalized quantum Fisher information and Schatten speed", Physical Review A 97 2, 022109 (2018).

[12] Zhihong Ren, Weidong Li, Augusto Smerzi, and Manuel Gessner, "Metrological Detection of Multipartite Entanglement from Young Diagrams", Physical Review Letters 126 8, 080502 (2021).

[13] Mingsheng Tian, Yu Xiang, Feng-Xiao Sun, Matteo Fadel, and Qiongyi He, "Characterizing Multipartite non-Gaussian Entanglement for a Three-Mode Spontaneous Parametric Down-Conversion Process", Physical Review Applied 18 2, 024065 (2022).

[14] Manuel Gessner, "Enhancement of the metrological sensitivity limit through knowledge of the average energy", Physical Review A 100 3, 032114 (2019).

[15] Gardo Blado, Francisco Herrera, and Joshuah Erwin, "Entanglement and the generalized uncertainty principle", Physics Essays 31 4, 397 (2018).

[16] Manuel Gessner, Luca Pezzè, and Augusto Smerzi, "Resolution-enhanced entanglement detection", Physical Review A 95 3, 032326 (2017).

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