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Maximally entangled states of (d,∞) quantum systems: some numerical studies

Identyfikatory
Warianty tytułu
PL
Maksymalne splątanie stanów kwantowych (d, ∞): wybrane studia numeryczne
Języki publikacji
EN
Abstrakty
EN
Gram matrix approach to an entanglement analysis of pure states describing (d, ∞) - quantum systems is being introduced. In particular, maximally entangled states are described as those having a special forms of the corresponding Gram matrices.
PL
W pracy zaprezentowano wstępną analizę czystych stanów kwantowych systemów typu (d, ∞). Omówiono stany maksymalnie splątane i opisano ich specjalną postać za pomocą pojęcia macierzy Grama.
Czasopismo
Rocznik
Strony
5--17
Opis fizyczny
Bibliogr. 29 poz.
Twórcy
  • University of Zielona Góra, Licealna 9, 65-417 Zielona Góra, Poland
  • University of Zielona Góra, Licealna 9, 65-417 Zielona Góra, Poland
Bibliografia
  • 1. Bengtsson I., Życzkowski К.: Geometry of Quantum States: An Introduction to Quantum Entanglement. Cambridge University Press, Cambridge, United Kingdom, 2006.
  • 2. Horodecki R., Horodecki P., Horodecki M., Horodecki K.: Quantum Entanglement. Rev. Mod. Phys., Vol. 81, pp. 865. Available at arXiv:quantphys:/0702225
  • 3. Guhne O., Toth G.: Entanglement Detection. 2008. Available at arXiv:quant-phys.70811280
  • 4. Horodecki R., Kilin S.Y., Kowalik J.S.: Quantum Cryptography and Computing. IOS Press, 2010.
  • 5. Witczak-Krempa W., Chen G., Kim Y.B., Balents L.: Correlated Quantum Phenomena in the Strong Spin-orbit Regime. Annual Review of Condensed Matter Physics, Vol. 5, No. I, 2013, pp. 57-82. Available at arXiv: 1305.2193v2
  • 6. You W.L., Horsch P., Oleś A.M.: Quantum Entanglement in the One-dimensional Spin-orbital SU(2) ® XXZ Model. Phys. Rev. B, Vol. 92, 2015, pp. 054423.
  • 7. Karimi E., Leach J., Slussarenko S., Piccirillo B., Marrucci L., Chen L., She W., Franke-Arnold S., Padgett M.J., Santamato E.: Spin-orbit Hybrid Entanglement of Photons and Quantum Contextuality. Phys. Rev. A, Vol. 82, No. 2, 2011, pp. 0221 15.
  • 8. Gielerak R.: Entangling Qubit with the Rest of the World - the Monogamy Principle in Action. Studia Informática, Vol. 38, No. 3, 2017, pp. 33-43.
  • 9. Castelvecchi D.: Quantum Cloud Goes Commercial. Nature, Vol. 543, 2017, pp. 159.
  • 10. IBM Makes Quantum Computing, 2016, Available on: https://www.rcsearch.ibm.com/ibm-q/
  • 11. Qiskit, 2019. Available on: https://github.com/IBM/qiskit-sdk-py
  • 12. Rigetti, Rigetti Launches Quantum Cloud Services, Announces $1-Million Challenge. HPCwire, 2018.
  • 13. Microsoft: Empowering the quantum revolution, 2019, Available on: https://www.microsoft.com/en-us/quantum/
  • 14. Google Research, Team & Focus Areas, Quantum, 2019, Available on: https://ai.google/research/teams/applied-science/quantum-ai/
  • 15. Intel Invests US $50 Million to Advance Quantum Computing. Intel Newsroom, 2015.
  • 16. D-Wave - The Quantum Computing Company: Meet D-Wave. Our Vision and History.
  • 17. 2019. Online: https://www.dwavesys.com/our-company/mcet-d-wavc
  • 18. Linke N.M., Maslov D., Roetteler M., Debnath S., Figgatt C., Landsman K.A., Wright K., Monroe C.: Experimental Comparison of two Quantum Computing Architectures. PNAS, Vol. I 14, 2017, pp. 3305-3310.
  • 19. Dcvoret M.H., Wallraff A., Martinis J.M.: Superconducting Qubits: A Short Review. 2014. Available at arXiv:cond-mat/04l1174
  • 20. DiVincenzo D.P.: The Physical Implementation of Quantum Computation. Fortschr. Phys., Vol. 48, 2000, pp. 771-783.
  • 21. Hazewinkel M., (cd.): Gram Matrix. Encyclopaedia of Mathematics, 2001.
  • 22. Gielerak, R.: Schmidt Decomposition of Mixed-pure States for (d, co) Systems and Some Applications, 2018. Available at arXiv: 1803.09541
  • 23. Gielerak, R.: in preparation 2019.
  • 24. Christensen O.: An Introduction to Frames and Riesz Bases. Springer Science, 2003.
  • 25. Prussing J.E.: The Principiai Minor Test for Scmidefinite Matrices. Journal of Guidance. Control and Dynamics, Vol. 1, 1986, pp. 121-122.
  • 26. Gilbert, G.T.: Positive Definite Matrices and Sylvester Sriterion. The American Mathematical Monthly, Vol. 98, No. 1 , 1991, pp. 44-46.
  • 27. Barends R., Kelly .1., Megrant A., Sank D., Jeffrey E., Chen Y., Yin Y., Chiaro B., Mutus J., Neill C., O'Malley P., Roushan P., Wenner J., White T.C., Cleland A.N., Martinis John M.: Coherent Josephson Qubit Suitable for Scalable Quantum Integrated Circuits. Phys. Rev. Lett., Vol. 111, No. 8, 2013, pp. 080502.
  • 28. Jankowski, N.: Comparison of Prototype Selection Algorithms Used in Construction of Neural Networks Learned by SVD. International Journal of Applied Mathematics and Computer Science, Vol. 28, No. 4, 2018, pp. 719-733.
  • 29. Lucińska M., Wierzchoń S.T.: Clustering Based on Eigenvectors of the Adjacency Matrix. International Journal of Applied Mathematics and Computer Science, Vol. 28, No. 4, 2018, pp. 771-786.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-bce78fee-ee80-491c-b6d9-eafbd76166b6
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