Optimal allocation of quantum resources

Roberto Salazar; Tanmoy Biswas; Jakub Czartowski; Karol Życzkowski; Paweł Horodecki

doi:10.22331/q-2021-03-10-407

Optimal allocation of quantum resources

Roberto Salazar^1,2, Tanmoy Biswas^1,3, Jakub Czartowski², Karol Życzkowski^2,4,5, and Paweł Horodecki^1,4,6

¹International Centre for Theory of Quantum Technologies, University of Gdansk, Wita Stwosza 63, 80-308 Gdansk, Poland
²Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków, Poland
³Institute of Theoretical Physics and Astrophysics, National Quantum Information Centre, Faculty of Mathematics, Physics and Informatics, University of Gdansk, Wita Stwosza 57, 80-308 Gdansk, Poland
⁴National Quantum Information Center of Gdansk, University of Gdansk, ul. Andersa 27 81-824 Sopot, Poland
⁵Centrum Fizyki Teoretycznej PAN, Al. Lotników 32/46, 02-668 Warszawa, Poland
⁶Faculty of Applied Physics and Mathematics, National Quantum Information Centre, Gdansk University of Technology, 80-233 Gdansk, Poland

Published:	2021-03-10, volume 5, page 407
Eprint:	arXiv:2006.16134v4
Doi:	https://doi.org/10.22331/q-2021-03-10-407
Citation:	Quantum 5, 407 (2021).

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

Abstract

The optimal allocation of resources is a crucial task for their efficient use in a wide range of practical applications in science and engineering. This paper investigates the optimal allocation of resources in multipartite quantum systems. In particular, we show the relevance of proportional fairness and optimal reliability criteria for the application of quantum resources. Moreover, we present optimal allocation solutions for an arbitrary number of qudits using measurement incompatibility as an exemplary resource theory. Besides, we study the criterion of optimal equitability and demonstrate its relevance to scenarios involving several resource theories such as nonlocality vs local contextuality. Finally, we highlight the potential impact of our results for quantum networks and other multi-party quantum information processing, in particular to the future Quantum Internet.

Featured image: The allocation of resources consists of distributing resources into a set of tasks according to a practical criterion. We can see in the figure a classic example of this problem: A castaway meditates on the optimal allocation of wood logs into several useful tasks: prepare a bonfire, build a ship, make a house or provide a fold for his flock. Our work introduces the study of the allocation of Quantum resources.

Popular summary

► BibTeX data

@article{Salazar2021optimalallocationof,
  doi = {10.22331/q-2021-03-10-407},
  url = {https://doi.org/10.22331/q-2021-03-10-407},
  title = {Optimal allocation of quantum resources},
  author = {Salazar, Roberto and Biswas, Tanmoy and Czartowski, Jakub and {\.{Z}}yczkowski, Karol and Horodecki, Pawe{\l{}}},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {407},
  month = mar,
  year = {2021}
}

► References

[1] R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys. 81, 865 (2009), URL: https://doi.org/10.1103/RevModPhys.81.865.
https://doi.org/10.1103/RevModPhys.81.865

[2] F. G. S. L. Brandão, M. Horodecki, J. Oppenheim, J. M. Renes, and R. W. Spekkens, Phys. Rev. Lett. 111, 250404 (2013), URL: https://doi.org/10.1103/PhysRevLett.111.250404.
https://doi.org/10.1103/PhysRevLett.111.250404

[3] E. Chitambar and G. Gour, Rev. Mod. Phys. 91, 025001 (2019), URL: https://doi.org/10.1103/RevModPhys.91.025001.
https://doi.org/10.1103/RevModPhys.91.025001

[4] J. Barrett, Phys. Rev. A 75, 032304 (2007), URL: https://doi.org/10.1103/PhysRevA.75.032304.
https://doi.org/10.1103/PhysRevA.75.032304

[5] R. Gallego and L. Aolita, Phys. Rev. X 5, 041008 (2015), URL: https://doi.org/10.1103/PhysRevX.5.041008.
https://doi.org/10.1103/PhysRevX.5.041008

[6] M. Allingham, M. L. Burstein, Resource Allocation and Economic Policy, Palgrave Macmillan UK (1976), URL: https://doi.org/10.1007/978-1-349-02673-9.
https://doi.org/10.1007/978-1-349-02673-9

[7] A. Kakhbod, Resource Allocation in Decentralized Systems with Strategic Agents: An Implementation Theory Approach( Springer-Verlag New York, 2013), URL: https://doi.org/10.1007/978-1-4614-6319-1.
https://doi.org/10.1007/978-1-4614-6319-1

[8] H. Luss, T. Russell Hsing, V. K. N. Lau, Equitable Resource Allocation, Models, Algorithms, and Applications (John Wiley and Sons, 2012).
https://www.wiley.com/en-us/Equitable+Resource+Allocation3A+Models2C+Algorithms+and+Applications-p-9781118054680

[9] I. A. Ushakov, Optimal Resource Allocation: With Practical Statistical Applications and Theory (John Wiley and Sons, 2013).
https://www.wiley.com/en-us/Optimal+Resource+Allocation3A+With+Practical+Statistical+Applications+and+Theory-p-9781118400708

[10] J. Bredin, R.T. Maheswaran , C. Imer, T. Basar, D. Kotz, D. Rus, 4th International Conference on Autonomous Agents.
https://experts.illinois.edu/en/publications/game-theoretic-formulation-of-multi-agent-resource-allocation

[11] Q. D. Lã, Y. H. Chew, B. Soong, Potential Game Theory, Applications in Radio Resource Allocation (Springer International Publishing, 2016), URL: https://doi.org/10.1007/978-3-319-30869-2.
https://doi.org/10.1007/978-3-319-30869-2

[12] L. Georgiadis, M. Neely, L. Tassiulas, Foundations and Trends in Networking: Vol. 1: No. 1, pp 1-144 (2006), URL: https://doi.org/10.1561/1300000001.
https://doi.org/10.1561/1300000001

[13] R. Matyssek, J. Koricheva, H. Schnyder, D. Ernst, J. C. Munch, W. Oßwald, H. Pretzsch, Growth and defense in Plants: Resource Allocation at multiple scale (Springer-Verlag , 2012), URL: https://doi.org/10.1007/978-3-642-30645-7.
https://doi.org/10.1007/978-3-642-30645-7

[14] P. Skrzypczyk, I. Šupić, and D. Cavalcanti, Phys. Rev. Lett. 122, 130403 (2019), URL: https://doi.org/10.1103/PhysRevLett.122.130403.
https://doi.org/10.1103/PhysRevLett.122.130403

[15] S. Designolle, M. Farkas, J. Kaniewski. New. J. Phys. 21 113053 (2019), URL: https://doi.org/10.1088/1367-2630/ab5020.
https://doi.org/10.1088/1367-2630/ab5020

[16] M. Oszmaniec and T. Biswas, Quantum 3, 133 (2019), URL: https://doi.org/10.22331/q-2019-04-26-133.
https://doi.org/10.22331/q-2019-04-26-133

[17] R. Uola, T. Kraft, J. Shang, X.-D. Yu, and O. Guhne, Phys. Rev. Lett. 122, 130404 (2019), https://doi.org/10.1103/PhysRevLett.122.130404.
https://doi.org/10.1103/PhysRevLett.122.130404

[18] R. Takagi and B. Regula, Phys. Rev. X 9, 031053 (2019), URL: https://doi.org/10.1103/PhysRevX.9.031053.
https://doi.org/10.1103/PhysRevX.9.031053

[19] P. Skrzypczyk and N. Linden, Phys. Rev. Lett. 122, 140403 (2019), URL: https://doi.org/10.1103/PhysRevLett.122.140403.
https://doi.org/10.1103/PhysRevLett.122.140403

[20] R. Takagi, B. Regula, K. Bu, Z.-W. Liu, and G. Adesso, Phys. Rev. Lett. 122, 140402 (2019), URL: https://doi.org/10.1103/PhysRevLett.122.140402.
https://doi.org/10.1103/PhysRevLett.122.140402

[21] C. Berge, Graphs and Hypergraphs (North-Holland Mathematical Library, 1973).
https://www.sciencedirect.com/bookseries/north-holland-mathematical-library/vol/6

[22] I. D. Ivanović, J. Phys. A: Math. Gen. 14, 3241 (1981), URL: https://doi.org/10.1088/0305-4470/14/12/019.
https://doi.org/10.1088/0305-4470/14/12/019

[23] W. K. Wootters and B. D. Fields, Ann. Phys. 191, 363 (1989), URL: https://doi.org/10.1016/0003-4916(89)90322-9.
https://doi.org/10.1016/0003-4916(89)90322-9

[24] D. McNulty, B. Pammer, and S. Weigert, J. Math. Phys. 57, 032202 (2016), URL: https://doi.org/10.1063/1.4943301.
https://doi.org/10.1063/1.4943301

[25] J. Czartowski, D. Goyeneche, K. Życzkowski, J. Phys. A: Math. Theor. 51, 305302 (2018), URL: https://doi.org/10.1088/1751-8121/aac973.
https://doi.org/10.1088/1751-8121/aac973

[26] M. Horodecki, P. Horodecki, and J. Oppenheim, Phys. Rev. A 67, 062104 (2003), URL: https://doi.org/10.1103/PhysRevA.67.062104.
https://doi.org/10.1103/PhysRevA.67.062104

[27] J. Oppenheim, M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. 89, 180402 (2002), URL: https://doi.org/10.1103/PhysRevLett.89.180402.
https://doi.org/10.1103/PhysRevLett.89.180402

[28] M. Horodecki, K. Horodecki, P. Horodecki, R. Horodecki, J. Oppenheim, A. Sen(De), and U. Sen, Phys. Rev. Lett. 90, 100402 (2003), URL: https://doi.org/10.1103/PhysRevLett.90.100402.
https://doi.org/10.1103/PhysRevLett.90.100402

[29] D. Yang, K. Horodecki, and A. Winter, Phys. Rev. Lett. 123, 170501 (2019), URL: https://doi.org/10.1103/PhysRevLett.123.170501.
https://doi.org/10.1103/PhysRevLett.123.170501

[30] K. Horodecki, M. Horodecki, P. Horodecki, and J. Oppenheim, Phys. Rev. Lett. 94, 160502 (2005), URL: https://doi.org/10.1103/PhysRevLett.94.160502.
https://doi.org/10.1103/PhysRevLett.94.160502

[31] F. G. S. L. Brandão, R. Ramanathan, A. Grudka, K. Horodecki, M. Horodecki, P. Horodecki, T. Szarek & H. Wojewódka, Nat Commun 7, 11345 (2016), URL: https://doi.org/10.1038/ncomms11345.
https://doi.org/10.1038/ncomms11345

[32] M. Kessler, R. Arnon-Friedman, IEEE Journal on Selected Areas in Information Theory, vol. 1, no. 2, pp. 568-584, URL: https://doi.org/10.1109/JSAIT.2020.3012498.
https://doi.org/10.1109/JSAIT.2020.3012498

[33] D. Saha, P. Horodecki and M. Pawłowski, New J. Phys. 21, 093057 (2019), URL: https://doi.org/10.1088/1367-2630/ab4149.
https://doi.org/10.1088/1367-2630/ab4149

[34] J.I. de Vicente, J. Phys. A: Math. Theor. 47, 424017 (2014), URL: https://doi.org/10.1088/1751-8113/47/42/424017.
https://doi.org/10.1088/1751-8113/47/42/424017

[35] K. Horodecki, A. Grudka, P. Joshi, W. Kłobus, J. Łodyga, Phys. Rev. A 92, 032104 (2015), URL: https://doi.org/10.1103/PhysRevA.92.032104.
https://doi.org/10.1103/PhysRevA.92.032104

[36] D. Saha and R. Ramanathan, Phys. Rev. A 95, 030104(R) (2017), URL: https://doi.org/10.1103/PhysRevA.95.030104.
https://doi.org/10.1103/PhysRevA.95.030104

[37] Kimble, H. J. Nature. 453 (7198): 1023– 1030 (2008), URL: https://doi.org/10.1038/nature07127.
https://doi.org/10.1038/nature07127

[38] R. Van Meter (2014), Quantum Networking (John Wiley and Sons, 2014).
https://www.wiley.com/en-us/Quantum+Networking-p-9781848215375

[39] N. Kalb, A. A. Reiserer, P. C. Humphreys, J. J. W. Bakermans, S. J. Kamerling, N. H. Nickerson, S. C. Benjamin, D. J. Twitchen, M. Markham, Science. 356 (6341): 928– 932 (2017), URL: https://doi.org/10.1126/science.aan0070.
https://doi.org/10.1126/science.aan0070

[40] S. Wehner, D. Elkouss, R. Hanson, Science Vol. 362, Issue 6412 (2018), URL: https://doi.org/10.1126/science.aam9288.
https://doi.org/10.1126/science.aam9288

[41] E. Kashefi and A. Pappa, Cryptography 1(2), 12 (2017), URL: https://doi.org/10.3390/cryptography1020012.
https://doi.org/10.3390/cryptography1020012

[42] S. Bravyi, D. Gosset, R.König, Science 362, Issue 308-311 (2018), URL: https://doi.org/10.1126/science.aar3106.
https://doi.org/10.1126/science.aar3106

[43] J. Czartowski, D. Goyeneche, M. Grassl, K. Życzkowski, Phys. Rev. Lett. 124, 090503 (2020), URL: https://doi.org/10.1103/PhysRevLett.124.090503.
https://doi.org/10.1103/PhysRevLett.124.090503

[44] M. Araujo, M. T. Quintino, C. Budroni, M. T. Cunha, and A. Cabello, Phys. Rev. A 88, 022118 (2013), URL: https://doi.org/10.1103/PhysRevA.82.022116.
https://doi.org/10.1103/PhysRevA.82.022116

[45] K. F. Pál and T. Vértesi, Phys. Rev. A 82, 022116 (2010), URL: https://doi.org/10.1103/PhysRevA.82.022116.
https://doi.org/10.1103/PhysRevA.82.022116

Cited by

[1] Domenico Ribezzo, Roberto Salazar, Jakub Czartowski, Flora Segur, Gianmarco Lemmi, Antoine Petitjean, Noel Farrugia, André Xuereb, Davide Bacco, and Alessandro Zavatta, "Quantum Random Access Codes Implementation for Resource Allocation and Coexistence with Classical Telecommunication", Advanced Quantum Technologies 7 4, 2300162 (2024).

The above citations are from Crossref's cited-by service (last updated successfully 2024-05-17 03:36:27). The list may be incomplete as not all publishers provide suitable and complete citation data.

On SAO/NASA ADS no data on citing works was found (last attempt 2024-05-17 03:36:27).

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.