Multiport based teleportation – transmission of a large amount of quantum information

Piotr Kopszak1, Marek Mozrzymas1, Michał Studziński2, and Michał Horodecki3

1Institute for Theoretical Physics, University of Wrocław 50-204 Wrocław, Poland
2Institute of Theoretical Physics and Astrophysics and National Quantum Information Centre in Gdańsk, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, 80-952 Gdańsk, Poland
3International Centre for Theory of Quantum Technologies, University of Gdańsk, 80-952, Poland

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We analyse the problem of transmitting a number of unknown quantum states or one composite system in one go. We derive a lower bound on the performance of such process, measured in the entanglement fidelity. The obtained bound is effectively computable and outperforms the explicit values of the entanglement fidelity calculated for the pre-existing variants of the port-based protocols, allowing for teleportation of a much larger amount of quantum information. The comparison with the exact formulas and similar analysis for the probabilistic scheme is also discussed. In particular, we present the closed-form expressions for the entanglement fidelity and for the probability of success in the probabilistic scheme in the qubit case in the picture of the spin angular momentum.

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[1] Ron M. Adin and Yuval Roichman. Enumeration of standard young tableaux, 2014. URL https:/​/​​abs/​1408.4497.

[2] A. C. Aitken. Xxvi.—the monomial expansion of determinantal symmetric functions. Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences, 61 (3): 300–310, 1943. 10.1017/​S0080454100006312.

[3] Leonardo Banchi, Jason Pereira, Seth Lloyd, and Stefano Pirandola. Convex optimization of programmable quantum computers. npj Quantum Information, 6 (1): 42, May 2020. ISSN 2056-6387. 10.1038/​s41534-020-0268-2.

[4] Salman Beigi and Robert König. Simplified instantaneous non-local quantum computation with applications to position-based cryptography. New Journal of Physics, 13 (9): 093036, 2011. ISSN 1367-2630. 10.1088/​1367-2630/​13/​9/​093036.

[5] Charles H. Bennett, Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres, and William K. Wootters. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Physical Review Letters, 70 (13): 1895–1899, March 1993. 10.1103/​PhysRevLett.70.1895.

[6] Andrew C. Berry. The accuracy of the gaussian approximation to the sum of independent variates. Transactions of the American Mathematical Society, 49 (1): 122–136, 1941. https:/​/​​10.1090/​S0002-9947-1941-0003498-3.

[7] Harry Buhrman, Łukasz Czekaj, Andrzej Grudka, Michał Horodecki, Paweł Horodecki, Marcin Markiewicz, Florian Speelman, and Sergii Strelchuk. Quantum communication complexity advantage implies violation of a Bell inequality. Proceedings of the National Academy of Sciences, 113 (12): 3191–3196, March 2016. ISSN 0027-8424, 1091-6490. 10.1073/​pnas.1507647113.

[8] Giulio Chiribella and Daniel Ebler. Quantum speedup in the identification of cause-effect relations. Nature Communications, 10: 1472, Apr 2019. 10.1038/​s41467-019-09383-8.

[9] Matthias Christandl, Felix Leditzky, Christian Majenz, Graeme Smith, Florian Speelman, and Michael Walter. Asymptotic performance of port-based teleportation. Communications in Mathematical Physics, 381 (1): 379–451, Jan 2021. ISSN 1432-0916. 10.1007/​s00220-020-03884-0.

[10] Carl-Gustav Esseen. On the liapunoff limit of error in the theory of probability. Arkiv för Matematik, Astronomi och Fysik A28, pages 1–19, 1942.

[11] Carl-Gustav Esseen. A moment inequality with an application to the central limit theorem. Scandinavian Actuarial Journal, 1956 (2): 160–170, 1956. 10.1080/​03461238.1956.10414946.

[12] W. Fulton. Young Tableaux. With Applications to Representation Theory and Geometry. Cambridge University Press, New York, 1997.

[13] W. Fulton and J. Harris. Representation Theory - A first Course. Springer-Verlag, New York, 1991.

[14] Satoshi Ishizaka and Tohya Hiroshima. Asymptotic Teleportation Scheme as a Universal Programmable Quantum Processor. Physical Review Letters, 101 (24): 240501, December 2008. 10.1103/​PhysRevLett.101.240501.

[15] Satoshi Ishizaka and Tohya Hiroshima. Quantum teleportation scheme by selecting one of multiple output ports. Physical Review A, 79 (4): 042306, April 2009. 10.1103/​PhysRevA.79.042306.

[16] Kabgyun Jeong, Jaewan Kim, and Soojoon Lee. Generalization of port-based teleportation and controlled teleportation capability. Phys. Rev. A, 102: 012414, Jul 2020. 10.1103/​PhysRevA.102.012414.

[17] Marek Mozrzymas, Michał Horodecki, and Michał Studziński. Structure and properties of the algebra of partially transposed permutation operators. Journal of Mathematical Physics, 55 (3): 032202, March 2014. ISSN 0022-2488, 1089-7658. 10.1063/​1.4869027.

[18] Marek Mozrzymas, Michał Studziński, and Michał Horodecki. A simplified formalism of the algebra of partially transposed permutation operators with applications. Journal of Physics A Mathematical General, 51 (12): 125202, Mar 2018a. 10.1088/​1751-8121/​aaad15.

[19] Marek Mozrzymas, Michał Studziński, Sergii Strelchuk, and Michał Horodecki. Optimal port-based teleportation. New Journal of Physics, 20 (5): 053006, May 2018b. 10.1088/​1367-2630/​aab8e7.

[20] Marek Mozrzymas, Michał Studziński, and Piotr Kopszak. Optimal Multi-port-based Teleportation Schemes. Quantum, 5: 477, June 2021. ISSN 2521-327X. 10.22331/​q-2021-06-17-477.

[21] M. Murao, D. Jonathan, M. B. Plenio, and V. Vedral. Quantum telecloning and multiparticle entanglement. Phys. Rev. A, 59: 156–161, Jan 1999. 10.1103/​PhysRevA.59.156.

[22] M. A. Nielsen and Isaac L. Chuang. Programmable quantum gate arrays. Phys. Rev. Lett., 79: 321–324, Jul 1997. 10.1103/​PhysRevLett.79.321.

[23] Jason Pereira, Leonardo Banchi, and Stefano Pirandola. Characterising port-based teleportation as universal simulator of qubit channels. 54 (20): 205301, apr 2021. 10.1088/​1751-8121/​abe67a.

[24] Stefano Pirandola, Riccardo Laurenza, Cosmo Lupo, and Jason L. Pereira. Fundamental limits to quantum channel discrimination. npj Quantum Information, 5: 50, Jun 2019. 10.1038/​s41534-019-0162-y.

[25] Marco Túlio Quintino, Qingxiuxiong Dong, Atsushi Shimbo, Akihito Soeda, and Mio Murao. Reversing unknown quantum transformations: Universal quantum circuit for inverting general unitary operations. Phys. Rev. Lett., 123: 210502, Nov 2019. 10.1103/​PhysRevLett.123.210502.

[26] Jona Schulz. The optimal Berry-Esseen constant in the binomial case. PhD thesis, University of Trier, 2016. URL https:/​/​​opus45-ubtr/​frontdoor/​deliver/​index/​docId/​732/​file/​Dissertation_Schulz.pdf.

[27] Michal Sedlák, Alessandro Bisio, and Mário Ziman. Optimal Probabilistic Storage and Retrieval of Unitary Channels. Physical Review Letters, 122 (17): 170502, May 2019. 10.1103/​PhysRevLett.122.170502.

[28] Sergii Strelchuk, Michał Horodecki, and Jonathan Oppenheim. Generalized Teleportation and Entanglement Recycling. Physical Review Letters, 110 (1): 010505, January 2013. 10.1103/​PhysRevLett.110.010505.

[29] Michał Studziński, Sergii Strelchuk, Marek Mozrzymas, and Michał Horodecki. Port-based teleportation in arbitrary dimension. Scientific Reports, 7: 10871, Sep 2017. 10.1038/​s41598-017-10051-4.

[30] Michał Studziński, Marek Mozrzymas, Piotr Kopszak, and Michał Horodecki. Efficient multi-port teleportation schemes, 2020. URL https:/​/​​abs/​2008.00984.

[31] Michał Studziński, Marek Mozrzymas, and Piotr Kopszak. Degradation of the resource state in port-based teleportation scheme, 2021. URL https:/​/​​abs/​2105.14886.

Cited by

[1] 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).

[2] Michal Studzinski, Marek Mozrzymas, Piotr Kopszak, and Michal Horodecki, "Efficient Multi Port-Based Teleportation Schemes", IEEE Transactions on Information Theory 68 12, 7892 (2022).

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

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

[5] Roman Gielerak and Marek Sawerwain, Lecture Notes in Computer Science 13827, 187 (2023) ISBN:978-3-031-30444-6.

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

[7] Marek Mozrzymas, Michał Studziński, and Piotr Kopszak, "Optimal Multi-port-based Teleportation Schemes", Quantum 5, 477 (2021).

[8] Eric Chitambar and Felix Leditzky, 2023 IEEE International Symposium on Information Theory (ISIT) 630 (2023) ISBN:978-1-6654-7554-9.

[9] Wan-Guan Chang, Chia-Yi Ju, Guang-Yin Chen, Yueh-Nan Chen, and Huan-Yu Ku, "Visually quantifying single-qubit quantum memory", Physical Review Research 6 2, 023035 (2024).

[10] R. Horodecki, "Quantum Information", Acta Physica Polonica A 139 3, 197 (2021).

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

[12] Dmitry Grinko and Maris Ozols, "Linear programming with unitary-equivariant constraints", arXiv:2207.05713, (2022).

[13] Felix Leditzky, "Optimality of the pretty good measurement for port-based teleportation", arXiv:2008.11194, (2020).

[14] Rivu Gupta, Shashank Gupta, Shiladitya Mal, and Aditi SenDe, "Performance of dense coding and teleportation for random states: Augmentation via preprocessing", Physical Review A 103 3, 032608 (2021).

[15] Quynh T. Nguyen, "The mixed Schur transform: efficient quantum circuit and applications", arXiv:2310.01613, (2023).

[16] Eric Chitambar and Felix Leditzky, "On the Duality of Teleportation and Dense Coding", arXiv:2302.14798, (2023).

[17] 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 2024-04-15 06:13:55) and SAO/NASA ADS (last updated successfully 2024-04-15 06:13:56). The list may be incomplete as not all publishers provide suitable and complete citation data.