Entangling qubit with the rest of the world – the monogamy principle in action

Roman Gieralak

Abstract


A simple derivation of the finite Schmidt decomposition of the pure states describing finite dimensional systems interacting with the infinite dimensional one is presented. In particular, maximally entangled pure states in such systems are being characterized.

Keywords


quantum entanglement; monogamy principle; Schmidt decomposition; spin-orbit entanglement

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References


Schrodinger E.: Die gegen wärtige Situation der Quantenmechanik. Naturwissenschaften, vol. 23, 807, 1935.

Nielsen M. A., Chuang I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge UK 2000.

Bengtsson I., Życzkowski K.: Geometry of Quantum States: An Introduction to Quantum Entanglement. Cambridge University Press, Cambridge UK 2006.

Horodecki R., Horodecki P., Horodecki M., Horodecki K.: Quantum Entanglement. Rev. Mod. Phys., vol. 81, 865, 2009, available at: arXiv:quantphys:/0702225.

Guhne O., Toth G.: Entanglement Detection, 2008, available at: arXiv:quant-phys:/0811280.

Horodecki R., Kilin S.Ya., Kowalik J.S. (edts.): Quantum Cryptography and Computing. IOS Press, 2010.

Condon E.U., Shortley G.H.: The Theory of Atomic Spectra. Cambridge University Press, 1935, ISBN 0-521-09209-4.

Griffiths J.: Introduction to Quantum Mechanics. Prentice Hall. 2nd edition, 2004.

Witczak-Krempa W., Gang Chen, Yong Baek Kim, Balents L.: Correlated Quantum Phenomena in the Strong Spin-orbit Regime, available at: arXiv:1305.2193v2

Wen-Long You, Horsch P., Oleś A.M.: Physical Review B 92, 054423, 2015.

Karimi E., Leach J., Slussarenko S., Piccirillo B., Marrucci L., Lixiang Chen, Weilong She, Franke-Arnold S., Padgett M.J., Santamato E.: Spin-orbit Hybrid Entanglement of Photons and Quantum Contextuality. Physical Review A 82 (2), 022115.

Georges A., de Medici L., Mravlje J.: Annual Review of Condensed Matter. Physics 4, 137, 2013.

Blanchard P., Bruning E.: Mathematical Methods in Physics. Birkhauser, Theorem 26.8, 2015, p. 387.

Reed M., Simon B.: Methods of Modern Mathematical Physics, Vol. 1: Functional Analysis. Academic Press, Berlin 1980, p. 50, ISBN 9780125850506.

Zhao Ming-Jing: Maximally Entangled States and Fully Entangled Fraction, available at: arXiv:1610.08147 v1

Gielerak R. (in preparation).

Gheorghiu V., Griffiths R.B.: Physics Rev. A 78, 020304 (R), 2008.

Nielsen M.A., Vidal G.: Majorisation and the Interconversion of Bipartite States. Quantum Information and Computation, vol. 1, no. 1, 2001, p. 76÷93.

Weyl H.: Das Asymptotische Verteilungsgesetz der Eigenwerte Linearer Partieller Differentialgleichungen. Math. Ann. 71, 1912, p. 441÷479.

Cavalcanti D., Brandao F.G.S.L., Terra Cunha M. O.: Are All Maximally Entangled States Pure? Physics Rev. A72 040303(R), 2005.




DOI: http://dx.doi.org/10.21936/si2017_v38.n3.808