Activation of genuine multipartite entanglement: Beyond the single-copy paradigm of entanglement characterisation

Hayata Yamasaki; Simon Morelli; Markus Miethlinger; Jessica Bavaresco; Nicolai Friis; Marcus Huber

doi:10.22331/q-2022-04-25-695

Activation of genuine multipartite entanglement: Beyond the single-copy paradigm of entanglement characterisation

Hayata Yamasaki^1,2, Simon Morelli^1,2, Markus Miethlinger¹, Jessica Bavaresco^1,2, Nicolai Friis^1,2, and Marcus Huber^2,1

¹Institute for Quantum Optics and Quantum Information — IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
²Atominstitut, Technische Universität Wien, Stadionallee 2, 1020 Vienna, Austria

Published:	2022-04-25, volume 6, page 695
Eprint:	arXiv:2106.01372v2
Doi:	https://doi.org/10.22331/q-2022-04-25-695
Citation:	Quantum 6, 695 (2022).

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Abstract

Entanglement shared among multiple parties presents complex challenges for the characterisation of different types of entanglement. One of the most fundamental insights is the fact that some mixed states can feature entanglement across every possible cut of a multipartite system yet can be produced via a mixture of states separable with respect to different partitions. To distinguish states that genuinely cannot be produced from mixing such partition-separable states, the term $\textit{genuine multipartite entanglement}$ was coined. All these considerations originate in a paradigm where only a single copy of the state is distributed and locally acted upon. In contrast, advances in quantum technologies prompt the question of how this picture changes when multiple copies of the same state become locally accessible. Here we show that multiple copies unlock genuine multipartite entanglement from partially separable states, i.e., mixtures of the partition-separable states, even from undistillable ensembles, and even more than two copies can be required to observe this effect. With these findings, we characterise the notion of genuine multipartite entanglement in the paradigm of multiple copies and conjecture a strict hierarchy of activatable states and an asymptotic collapse of the hierarchy.

Popular summary

A centrally important concept in multipartite entanglement theory is the distinction between biseparability and genuine multipartite entanglement (GME). Here, we show that multiple identically prepared copies of biseparable states, readily available in many quantum communication technologies, can result in GME. Indeed, sometimes more than two copies are needed for this to happen, yet, GME activation may occur for states with no distillable bipartite entanglement. Our results thus shed new light on, and even call into question, basic tenets of entanglement theory, and significantly advance the field of multipartite entanglement characterisation by opening up a new frontier beyond the single-copy paradigm.

► BibTeX data

@article{Yamasaki2022activationofgenuine,
  doi = {10.22331/q-2022-04-25-695},
  url = {https://doi.org/10.22331/q-2022-04-25-695},
  title = {Activation of genuine multipartite entanglement: {B}eyond the single-copy paradigm of entanglement characterisation},
  author = {Yamasaki, Hayata and Morelli, Simon and Miethlinger, Markus and Bavaresco, Jessica and Friis, Nicolai and Huber, Marcus},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {695},
  month = apr,
  year = {2022}
}

► References

[1] Jonathan P. Dowling and Gerard J. Milburn, Quantum technology: the second quantum revolution, Phil. Trans. R. Soc. A 361, 1655 (2003), arXiv:quant-ph/0206091.
https://doi.org/10.1098/rsta.2003.1227
arXiv:quant-ph/0206091

[2] Michael Epping, Hermann Kampermann, Chiara Macchiavello, and Dagmar Bruß, Multi-partite entanglement can speed up quantum key distribution in networks, New J. Phys. 19, 093012 (2017), arXiv:1612.05585.
https://doi.org/10.1088/1367-2630/aa8487
arXiv:1612.05585

[3] Matej Pivoluska, Marcus Huber, and Mehul Malik, Layered quantum key distribution, Phys. Rev. A 97, 032312 (2018), arXiv:1709.00377.
https://doi.org/10.1103/PhysRevA.97.032312
arXiv:1709.00377

[4] Jérémy Ribeiro, Gláucia Murta, and Stephanie Wehner, Fully device-independent conference key agreement, Phys. Rev. A 97, 022307 (2018), arXiv:1708.00798.
https://doi.org/10.1103/PhysRevA.97.022307
arXiv:1708.00798

[5] Stefan Bäuml and Koji Azuma, Fundamental limitation on quantum broadcast networks, Quantum Sci. Technol. 2, 024004 (2017), arXiv:1609.03994.
https://doi.org/10.1088/2058-9565/aa6d3c
arXiv:1609.03994

[6] Géza Tóth, Multipartite entanglement and high-precision metrology, Phys. Rev. A 85, 022322 (2012), arXiv:1006.4368.
https://doi.org/10.1103/PhysRevA.85.022322
arXiv:1006.4368

[7] Andrew J. Scott, Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions, Phys. Rev. A 69, 052330 (2004), arXiv:quant-ph/0310137.
https://doi.org/10.1103/PhysRevA.69.052330
arXiv:quant-ph/0310137

[8] Dagmar Bruß and Chiara Macchiavello, Multipartite entanglement in quantum algorithms, Phys. Rev. A 83, 052313 (2011), arXiv:1007.4179.
https://doi.org/10.1103/PhysRevA.83.052313
arXiv:1007.4179

[9] Robert Raussendorf and Hans J. Briegel, A One-Way Quantum Computer, Phys. Rev. Lett. 86, 5188 (2001), arXiv:quant-ph/0010033.
https://doi.org/10.1103/PhysRevLett.86.5188
arXiv:quant-ph/0010033

[10] Hans J. Briegel and Robert Raussendorf, Persistent Entanglement in Arrays of Interacting Particles, Phys. Rev. Lett. 86, 910 (2001), arXiv:quant-ph/0004051.
https://doi.org/10.1103/PhysRevLett.86.910
arXiv:quant-ph/0004051

[11] Leonid Gurvits, Classical complexity and quantum entanglement, J. Comput. Syst. Sci. 69, 448 (2004), Special Issue on STOC 2003, arXiv:quant-ph/0303055.
https://doi.org/10.1016/j.jcss.2004.06.003
arXiv:quant-ph/0303055

[12] F. Verstraete, J. Dehaene, B. De Moor, and H. Verschelde, Four qubits can be entangled in nine different ways, Phys. Rev. A 65, 052112 (2002), arXiv:quant-ph/0109033.
https://doi.org/10.1103/PhysRevA.65.052112
arXiv:quant-ph/0109033

[13] Andreas Osterloh and Jens Siewert, Constructing $n$-qubit entanglement monotones from antilinear operators, Phys. Rev. A 72, 012337 (2005), arXiv:quant-ph/0410102.
https://doi.org/10.1103/PhysRevA.72.012337
arXiv:quant-ph/0410102

[14] Julio I. de Vicente, Cornelia Spee, and Barbara Kraus, Maximally Entangled Set of Multipartite Quantum States, Phys. Rev. Lett. 111, 110502 (2013), arXiv:1305.7398.
https://doi.org/10.1103/PhysRevLett.111.110502
arXiv:1305.7398

[15] Katharina Schwaiger, David Sauerwein, Martí Cuquet, Julio I. de Vicente, and Barbara Kraus, Operational Multipartite Entanglement Measures, Phys. Rev. Lett. 115, 150502 (2015), arXiv:1503.00615.
https://doi.org/10.1103/PhysRevLett.115.150502
arXiv:1503.00615

[16] Julio I. de Vicente, Cornelia Spee, David Sauerwein, and Barbara Kraus, Entanglement manipulation of multipartite pure states with finite rounds of classical communication, Phys. Rev. A 95, 012323 (2017), arXiv:1607.05145.
https://doi.org/10.1103/PhysRevA.95.012323
arXiv:1607.05145

[17] C. Spee, J. I. de Vicente, D. Sauerwein, and B. Kraus, Entangled Pure State Transformations via Local Operations Assisted by Finitely Many Rounds of Classical Communication, Phys. Rev. Lett. 118, 040503 (2017), arXiv:1606.04418.
https://doi.org/10.1103/PhysRevLett.118.040503
arXiv:1606.04418

[18] David Sauerwein, Nolan R. Wallach, Gilad Gour, and Barbara Kraus, Transformations among Pure Multipartite Entangled States via Local Operations are Almost Never Possible, Phys. Rev. X 8, 031020 (2018), arXiv:1711.11056.
https://doi.org/10.1103/PhysRevX.8.031020
arXiv:1711.11056

[19] Géza Tóth and Otfried Gühne, Entanglement detection in the stabilizer formalism, Phys. Rev. A 72, 022340 (2005), arXiv:quant-ph/0501020.
https://doi.org/10.1103/PhysRevA.72.022340
arXiv:quant-ph/0501020

[20] Nicolai Friis, Giuseppe Vitagliano, Mehul Malik, and Marcus Huber, Entanglement Certification From Theory to Experiment, Nat. Rev. Phys. 1, 72 (2019), arXiv:1906.10929.
https://doi.org/10.1038/s42254-018-0003-5
arXiv:1906.10929

[21] Nicolai Friis, Oliver Marty, Christine Maier, Cornelius Hempel, Milan Holzäpfel, Petar Jurcevic, Martin B. Plenio, Marcus Huber, Christian Roos, Rainer Blatt, and Ben Lanyon, Observation of Entangled States of a Fully Controlled 20-Qubit System, Phys. Rev. X 8, 021012 (2018), arXiv:1711.11092.
https://doi.org/10.1103/PhysRevX.8.021012
arXiv:1711.11092

[22] Michał Horodecki, Paweł Horodecki, and Ryszard Horodecki, Separability of mixed states: necessary and sufficient conditions, Phys. Lett. A 223, 25 (1996), arXiv:quant-ph/9605038.
https://doi.org/10.1016/S0375-9601(96)00706-2
arXiv:quant-ph/9605038

[23] Asher Peres, Separability Criterion for Density Matrices, Phys. Rev. Lett. 77, 1413 (1996), arXiv:quant-ph/9604005.
https://doi.org/10.1103/PhysRevLett.77.1413
arXiv:quant-ph/9604005

[24] Marcus Huber and Ritabrata Sengupta, Witnessing Genuine Multipartite Entanglement with Positive Maps, Phys. Rev. Lett. 113, 100501 (2014), arXiv:1404.7449.
https://doi.org/10.1103/PhysRevLett.113.100501
arXiv:1404.7449

[25] Fabien Clivaz, Marcus Huber, Ludovico Lami, and Gláucia Murta, Genuine-multipartite entanglement criteria based on positive maps, J. Math. Phys. 58, 082201 (2017), arXiv:1609.08126.
https://doi.org/10.1063/1.4998433
arXiv:1609.08126

[26] Andrea Rodriguez-Blanco, Alejandro Bermudez, Markus Müller, and Farid Shahandeh, Efficient and Robust Certification of Genuine Multipartite Entanglement in Noisy Quantum Error Correction Circuits, PRX Quantum 2, 020304 (2021), arXiv:2010.02941.
https://doi.org/10.1103/PRXQuantum.2.020304
arXiv:2010.02941

[27] Siddarth Koduru Joshi, Djeylan Aktas, Sören Wengerowsky, Martin Lončarić, Sebastian Philipp Neumann, Bo Liu, Thomas Scheidl, Guillermo Currás Lorenzo, Željko Samec, Laurent Kling, Alex Qiu, Mohsen Razavi, Mario Stipčević, John G. Rarity, and Rupert Ursin, A trusted node–free eight-user metropolitan quantum communication network, Sci. Adv. 6 (2020), arXiv:1907.08229.
https://doi.org/10.1126/sciadv.aba0959
arXiv:1907.08229

[28] Sören Wengerowsky, Siddarth Koduru Joshi, Fabian Steinlechner, Hannes Hübel, and Rupert Ursin, An entanglement-based wavelength-multiplexed quantum communication network, Nature 564, 225 (2018), arXiv:1801.06194.
https://doi.org/10.1038/s41586-018-0766-y
arXiv:1801.06194

[29] Sebastian Ecker, Frédéric Bouchard, Lukas Bulla, Florian Brandt, Oskar Kohout, Fabian Steinlechner, Robert Fickler, Mehul Malik, Yelena Guryanova, Rupert Ursin, and Marcus Huber, Overcoming Noise in Entanglement Distribution, Phys. Rev. X 9, 041042 (2019), arXiv:1904.01552.
https://doi.org/10.1103/PhysRevX.9.041042
arXiv:1904.01552

[30] Xiao-Min Hu, Wen-Bo Xing, Bi-Heng Liu, Yun-Feng Huang, Chuan-Feng Li, Guang-Can Guo, Paul Erker, and Marcus Huber, Efficient generation of high-dimensional entanglement through multipath down-conversion, Phys. Rev. Lett. 125, 090503 (2020), arXiv:2004.09964.
https://doi.org/10.1103/PhysRevLett.125.090503
arXiv:2004.09964

[31] Hayata Yamasaki, Alexander Pirker, Mio Murao, Wolfgang Dür, and Barbara Kraus, Multipartite entanglement outperforming bipartite entanglement under limited quantum system sizes, Phys. Rev. A 98, 052313 (2018), arXiv:1808.00005.
https://doi.org/10.1103/PhysRevA.98.052313
arXiv:1808.00005

[32] Miguel Navascues, Elie Wolfe, Denis Rosset, and Alejandro Pozas-Kerstjens, Genuine Network Multipartite Entanglement, Phys. Rev. Lett. 125, 240505 (2020), arXiv:2002.02773.
https://doi.org/10.1103/PhysRevLett.125.240505
arXiv:2002.02773

[33] Tristan Kraft, Sébastien Designolle, Christina Ritz, Nicolas Brunner, Otfried Gühne, and Marcus Huber, Quantum entanglement in the triangle network, Phys. Rev. A 103, L060401 (2021), arXiv:2002.03970.
https://doi.org/10.1103/PhysRevA.103.L060401
arXiv:2002.03970

[34] Gláucia Murta, Federico Grasselli, Hermann Kampermann, and Dagmar Bruß, Quantum conference key agreement: A review, Adv. Quantum Technol. 3, 2000025 (2020), arXiv:2003.10186.
https://doi.org/10.1002/qute.202000025
arXiv:2003.10186

[35] Marcus Huber and Martin Plesch, Purification of genuine multipartite entanglement, Phys. Rev. A 83, 062321 (2011), arXiv:1103.4294.
https://doi.org/10.1103/PhysRevA.83.062321
arXiv:1103.4294

[36] Otfried Gühne and Géza Tóth, Entanglement detection, Phys. Rep. 474, 1 (2009), arXiv:0811.2803.
https://doi.org/10.1016/j.physrep.2009.02.004
arXiv:0811.2803

[37] Szilárd Szalay, $k$-stretchability of entanglement, and the duality of $k$-separability and $k$-producibility, Quantum 3, 204 (2019), arXiv:1906.10798.
https://doi.org/10.22331/q-2019-12-02-204
arXiv:1906.10798

[38] Seyed Mohammad Hashemi Rafsanjani, Marcus Huber, Curtis J. Broadbent, and Joseph H. Eberly, Genuinely multipartite concurrence of $N$-qubit $X$ matrices, Phys. Rev. A 86, 062303 (2012), arXiv:1208.2706.
https://doi.org/10.1103/PhysRevA.86.062303
arXiv:1208.2706

[39] Zhi-Hao Ma, Zhi-Hua Chen, Jing-Ling Chen, Christoph Spengler, Andreas Gabriel, and Marcus Huber, Measure of genuine multipartite entanglement with computable lower bounds, Phys. Rev. A 83, 062325 (2011), arXiv:1101.2001.
https://doi.org/10.1103/PhysRevA.83.062325
arXiv:1101.2001

[40] Ludovico Lami and Marcus Huber, Bipartite depolarizing channels, J. Math. Phys. 57, 092201 (2016), arXiv:1603.02158.
https://doi.org/10.1063/1.4962339
arXiv:1603.02158

[41] David Schmid, Denis Rosset, and Francesco Buscemi, The type-independent resource theory of local operations and shared randomness, Quantum 4, 262 (2020), arXiv:1909.04065.
https://doi.org/10.22331/q-2020-04-30-262
arXiv:1909.04065

[42] Kohdai Kuroiwa and Hayata Yamasaki, General Quantum Resource Theories: Distillation, Formation and Consistent Resource Measures, Quantum 4, 355 (2020), arXiv:2002.02458.
https://doi.org/10.22331/q-2020-11-01-355
arXiv:2002.02458

[43] Kohdai Kuroiwa and Hayata Yamasaki, Asymptotically consistent measures of general quantum resources: Discord, non-Markovianity, and non-Gaussianity, Phys. Rev. A 104, L020401 (2021), arXiv:2103.05665.
https://doi.org/10.1103/PhysRevA.104.L020401
arXiv:2103.05665

Cited by

[1] Carlos Palazuelos and Julio I. de Vicente, "Genuine multipartite entanglement of quantum states in the multiple-copy scenario", Quantum 6, 735 (2022).

[2] Simon Morelli, David Sauerwein, Michalis Skotiniotis, and Nicolai Friis, "Metrology-assisted entanglement distribution in noisy quantum networks", Quantum 6, 722 (2022).

[3] 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).

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