Optimal Multi-port-based Teleportation Schemes

Marek Mozrzymas; Michał Studziński; Piotr Kopszak

doi:10.22331/q-2021-06-17-477

Optimal Multi-port-based Teleportation Schemes

Marek Mozrzymas¹, Michał Studziński², and Piotr Kopszak¹

¹Institute for Theoretical Physics, University of Wrocław, 50-204 Wrocław, Poland
²Institute of Theoretical Physics and Astrophysics, National Quantum Information Centre, University of Gdańsk, 80-952 Gdańsk, Poland

Published:	2021-06-17, volume 5, page 477
Eprint:	arXiv:2011.09256v3
Doi:	https://doi.org/10.22331/q-2021-06-17-477
Citation:	Quantum 5, 477 (2021).

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Abstract

In this paper, we introduce optimal versions of a multi-port based teleportation scheme allowing to send a large amount of quantum information. We fully characterise probabilistic and deterministic case by presenting expressions for the average probability of success and entanglement fidelity. In the probabilistic case, the final expression depends only on global parameters describing the problem, such as the number of ports $N$, the number of teleported systems $k$, and local dimension $d$. It allows us to show square improvement in the number of ports with respect to the non-optimal case. We also show that the number of teleported systems can grow when the number $N$ of ports increases as $o(N)$ still giving high efficiency. In the deterministic case, we connect entanglement fidelity with the maximal eigenvalue of a generalised teleportation matrix. In both cases the optimal set of measurements and the optimal state shared between sender and receiver is presented. All the results are obtained by formulating and solving primal and dual SDP problems, which due to existing symmetries can be solved analytically. We use extensively tools from representation theory and formulate new results that could be of the separate interest for the potential readers.

► BibTeX data

@article{Mozrzymas2021optimalmultiport,
  doi = {10.22331/q-2021-06-17-477},
  url = {https://doi.org/10.22331/q-2021-06-17-477},
  title = {Optimal {M}ulti-port-based {T}eleportation {S}chemes},
  author = {Mozrzymas, Marek and Studzi{\'{n}}ski, Micha{\l{}} and Kopszak, Piotr},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {477},
  month = jun,
  year = {2021}
}

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Cited by

[1] Felix Leditzky, "Optimality of the pretty good measurement for port-based teleportation", Letters in Mathematical Physics 112 5, 98 (2022).

[2] Sergii Strelchuk and Michał Studziński, "Minimal port-based teleportation", New Journal of Physics 25 6, 063012 (2023).

[3] Armin Tavakoli, Alejandro Pozas-Kerstjens, Peter Brown, and Mateus Araújo, "Semidefinite programming relaxations for quantum correlations", Reviews of Modern Physics 96 4, 045006 (2024).

[4] Dmitry Grinko and Maris Ozols, "Linear Programming with Unitary-Equivariant Constraints", Communications in Mathematical Physics 405 12, 278 (2024).

[5] Marek Mozrzymas, Michał Horodecki, and Michał Studziński, "From port-based teleportation to Frobenius reciprocity theorem: partially reduced irreducible representations and their applications", Letters in Mathematical Physics 114 2, 56 (2024).

[6] Maria Balanzó-Juandó, Michał Studziński, and Felix Huber, "Positive maps from the walled Brauer algebra", Journal of Physics A: Mathematical and Theoretical 57 11, 115202 (2024).

[7] Daniel Collins, "Teleportation of Post-Selected Quantum States", Quantum 8, 1280 (2024).

[8] Adam Wills, Min-Hsiu Hsieh, and Sergii Strelchuk, "Efficient Algorithms for All Port-Based Teleportation Protocols", PRX Quantum 5 3, 030354 (2024).

[9] Piotr Kopszak, Marek Mozrzymas, Michał Studziński, and Michał Horodecki, "Multiport based teleportation – transmission of a large amount of quantum information", Quantum 5, 576 (2021).

[10] Marco Túlio Quintino, "Quantum teleportation beyond its standard form: Multi-Port-Based Teleportation", Quantum Views 5, 56 (2021).

[11] Michał Studziński, Marek Mozrzymas, and Piotr Kopszak, "Square-root measurements and degradation of the resource state in port-based teleportation scheme", Journal of Physics A: Mathematical and Theoretical 55 37, 375302 (2022).

[12] Xiao-Min Hu, Yu Guo, Bi-Heng Liu, Chuan-Feng Li, and Guang-Can Guo, "Progress in quantum teleportation", Nature Reviews Physics 5 6, 339 (2023).

[13] Dmitry Grinko, Adam Burchardt, and Maris Ozols, "Gelfand-Tsetlin basis for partially transposed permutations, with applications to quantum information", arXiv:2310.02252, (2023).

[14] Michał Studziński, Tomasz Młynik, Marek Mozrzymas, and Michał Horodecki, "Irreducible matrix representations for the walled Brauer algebra", arXiv:2501.13067, (2025).

[15] Dmitry Grinko, Adam Burchardt, and Maris Ozols, "Efficient quantum circuits for port-based teleportation", arXiv:2312.03188, (2023).

The above citations are from Crossref's cited-by service (last updated successfully 2025-03-24 02:00:54) and SAO/NASA ADS (last updated successfully 2025-03-24 02:00:54). The list may be incomplete as not all publishers provide suitable and complete citation data.

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Optimal Multi-port-based Teleportation Schemes

Abstract

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