Genuine multipartite entanglement of quantum states in the multiple-copy scenario

Carlos Palazuelos; Julio I. de Vicente

doi:10.22331/q-2022-06-13-735

Genuine multipartite entanglement of quantum states in the multiple-copy scenario

Carlos Palazuelos^1,2 and Julio I. de Vicente³

¹Departamento de Análisis Matemático y Matemática Aplicada, Universidad Complutense de Madrid, E-28040 Madrid, Spain
²Instituto de Ciencias Matemáticas, E-28049 Madrid, Spain
³Departamento de Matemáticas, Universidad Carlos III de Madrid, E-28911, Leganés (Madrid), Spain

Published:	2022-06-13, volume 6, page 735
Eprint:	arXiv:2201.08694v3
Doi:	https://doi.org/10.22331/q-2022-06-13-735
Citation:	Quantum 6, 735 (2022).

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

Genuine multipartite entanglement (GME) is considered a powerful form of entanglement since it corresponds to those states that are not biseparable, i.e. a mixture of partially separable states across different bipartitions of the parties. In this work we study this phenomenon in the multiple-copy regime, where many perfect copies of a given state can be produced and controlled. In this scenario the above definition leads to subtle intricacies as biseparable states can be GME-activatable, i.e. several copies of a biseparable state can display GME. We show that the set of GME-activatable states admits a simple characterization: a state is GME-activatable if and only if it is not partially separable across one bipartition of the parties. This leads to the second question of whether there is a general upper bound in the number of copies that needs to be considered in order to observe the activation of GME, which we answer in the negative. In particular, by providing an explicit construction, we prove that for any number of parties and any number $k\in\mathbb{N}$ there exist GME-activatable multipartite states of fixed (i.e. independent of $k$) local dimensions such that $k$ copies of them remain biseparable.

► BibTeX data

@article{Palazuelos2022genuinemultipartite,
  doi = {10.22331/q-2022-06-13-735},
  url = {https://doi.org/10.22331/q-2022-06-13-735},
  title = {Genuine multipartite entanglement of quantum states in the multiple-copy scenario},
  author = {Palazuelos, Carlos and Vicente, Julio I. de},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {735},
  month = jun,
  year = {2022}
}

► References

[1] V. Giovannetti, S. Lloyd, and L. Maccone, Nature Photonics 5, 222 (2011).
https://doi.org/10.1038/nphoton.2011.35

[2] G. Tóth and I. Apellaniz, J. Phys. A: Math. Theor. 47, 424006 (2014).
https://doi.org/10.1088/1751-8113/47/42/424006

[3] G. Murta, F. Grasselli, H. Kampermann, and D. Bruß, Adv. Quantum Technol. 3, 2000025 (2020).
https://doi.org/10.1002/qute.202000025

[4] R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. 86, 5188 (2001).
https://doi.org/10.1103/PhysRevLett.86.5188

[5] O. Gühne and G. Tóth, Phys. Rep. 474, 1 (2009).
https://doi.org/10.1016/j.physrep.2009.02.004

[6] N. Friis, G. Vitagliano, M. Malik, and M. Huber, Nat. Rev. Phys. 1, 72 (2019).
https://doi.org/10.1038/s42254-018-0003-5

[7] L. Gurvits, J. Comput. Syst. Sci. 69, 448 (2004).
https://doi.org/10.1016/j.jcss.2004.06.003

[8] W. Dür, G. Vidal, and J.I. Cirac, Phys. Rev. A 62, 062314 (2000).
https://doi.org/10.1103/PhysRevA.62.062314

[9] F. Verstraete, J. Dehaene, B. De Moor, and H. Verschelde, Phys. Rev. A, 65, 052112 (2002).
https://doi.org/10.1103/PhysRevA.65.052112

[10] E. Briand, J.-G. Luque, J.-Y. Thibon, F. Verstraete, J. Math. Phys. 45, 4855 (2004).
https://doi.org/10.1063/1.1809255

[11] J. I. de Vicente, C. Spee, and B. Kraus, Phys. Rev. Lett. 111, 110502 (2013).
https://doi.org/10.1103/PhysRevLett.111.110502

[12] C. Spee, J. I. de Vicente, and B. Kraus, J. Math. Phys. 57, 052201 (2016).
https://doi.org/10.1063/1.4946895

[13] D. Sauerwein, N. R. Wallach, G. Gour, and B. Kraus, Phys. Rev. X 8, 031020 (2018).
https://doi.org/10.1103/PhysRevX.8.031020

[14] M. Seevinck and J. Uffink, Phys. Rev. A 65, 012107 (2001).
https://doi.org/10.1103/PhysRevA.65.012107

[15] N. Friis, O. Marty, C. Maier, C. Hempel, M. Holzäpfel, P. Jurcevic, M. B. Plenio, M. Huber, C. Roos, R. Blatt, and B. Lanyon, Phys. Rev. X 8, 021012 (2018).
https://doi.org/10.1103/PhysRevX.8.021012

[16] P. Hyllus, W. Laskowski, R. Krischek, C. Schwemmer, W. Wieczorek, H. Weinfurter, L. Pezzé, and A. Smerzi, Phys. Rev. A 85, 022321 (2012).
https://doi.org/10.1103/PhysRevA.85.022321

[17] G. Tóth, Phys. Rev. A 85, 022322 (2012).
https://doi.org/10.1103/PhysRevA.85.022322

[18] S. Das, S. Bäuml, M. Winczewski, and K. Horodecki, Phys. Rev. X 11, 041016 (2021).
https://doi.org/10.1103/PhysRevX.11.041016

[19] M. Huber and M. Plesch, Phys. Rev. A 83, 062321 (2011).
https://doi.org/10.1103/PhysRevA.83.062321

[20] G. Carrara, H. Kampermann, D. Bruß, and G. Murta, Phys. Rev. Research 3, 013264 (2021).
https://doi.org/10.1103/PhysRevResearch.3.013264

[21] D. Cavalcanti, M. L. Almeida, V. Scarani, and A. Acin, Nat. Commun. 2, 184 (2011).
https://doi.org/10.1038/ncomms1193

[22] P. Contreras-Tejada, C. Palazuelos, and J. I. de Vicente, Phys. Rev. Lett. 126, 040501 (2021).
https://doi.org/10.1103/PhysRevLett.126.040501

[23] C. Palazuelos, Phys. Rev. Lett. 109, 190401 (2012).
https://doi.org/10.1103/PhysRevLett.109.190401

[24] G. Smith and J. Yard, Science 321, 1812 (2008).
https://doi.org/10.1126/science.1162242

[25] M. Navascues, E. Wolfe, D. Rosset, and A. Pozas-Kerstjens, Phys. Rev. Lett. 125, 240505 (2020).
https://doi.org/10.1103/PhysRevLett.125.240505

[26] H. Yamasaki, S. Morelli, M. Miethlinger, J. Bavaresco, N. Friis, and M. Huber, Quantum 6, 695 (2022).
https://doi.org/10.22331/q-2022-04-25-695

[27] T. Kraft, C. Ritz, N. Brunner, M. Huber, and O. Gühne, Phys. Rev. Lett. 120, 060502 (2018).
https://doi.org/10.1103/PhysRevLett.120.060502

[28] V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, Phys. Rev. Lett. 78, 2275 (1997).
https://doi.org/10.1103/PhysRevLett.78.2275

[29] S. Beigi and P. W. Shor, J. Math. Phys. 51, 042202 (2010).
https://doi.org/10.1063/1.3364793

[30] M. Horodecki and P Horodecki, Phys. Rev. A 59, 4206 (1999).
https://doi.org/10.1103/PhysRevA.59.4206

[31] L. Gurvits and H. Barnum, Phys. Rev. A 66, 062311 (2002).
https://doi.org/10.1103/PhysRevA.66.062311

[32] R. Schneider. Convex Bodies: The Brunn-Minkowski Theory. Encyclopedia of Mathematics and its Applications. Cambridge University Press, 2nd edition, 2013.
https://doi.org/10.1017/CBO9781139003858

[33] P. Contreras-Tejada, C. Palazuelos, and J. I. de Vicente, Phys. Rev. Lett. 128, 220501 (2022).
https://doi.org/10.1103/PhysRevLett.128.220501

[34] K. Azuma, S. Bäuml, T. Coopmans, D. Elkouss, and B. Li, AVS Quantum Sci. 3, 014101 (2021).
https://doi.org/10.1116/5.0024062

[35] G. Vardoyan, S. Guha, P. Nain, and D. Towsley, ACM SIGMETRICS Perform. Eval. Rev. 47, 27 (2019).
https://doi.org/10.1145/3374888.3374899

Cited by

[1] Marcel Seelbach Benkner, Jens Siewert, Otfried Gühne, and Gael Sentís, "Characterizing generalized axisymmetric quantum states in d×d systems", Physical Review A 106 2, 022415 (2022).

[2] Jonathan Schluck, Gláucia Murta, Hermann Kampermann, Dagmar Bruß, and Nikolai Wyderka, "Continuity of robustness measures in quantum resource theories", Journal of Physics A: Mathematical and Theoretical 56 25, 255303 (2023).

The above citations are from Crossref's cited-by service (last updated successfully 2023-12-06 21:45:08) and SAO/NASA ADS (last updated successfully 2023-12-06 21:45:09). The list may be incomplete as not all publishers provide suitable and complete citation data.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.