Abstract
This is a report on some new results concerning entanglement. Entanglement is not envisioned here only as an algebraic property for the state of a compound system, but also as a topological property when one subsystem, acting as a “measuring” device, is macroscopic. These topological properties have also their own dynamics and show a local behavior in the generation, growth and transport of entanglement, which can be described mathematically in some detail.
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References
Schrödinger, E.: Discussion of probability relations in separated systems. Proc. Camb. Philos. Soc. 31, 555 (1935); 32, 446 (1936)
Schrödinger, E.: Die gegenwärtige Situation in der Quantenmechanik. Naturwissensschaften 23, 807, 823, 844 (1935); reprinted in Wheeler, J.A, Zurek, W.H.: Quantum Mechanics and Measurement. Princeton University Press, Princeton (1983)
von Neumann, J.: Mathematische Grundlagen der Quantenmechanik. Springer, Berlin (1932)
Laloë, F.: Comprenons-nous vraiment la mécanique quantique? CNRS Editions. EDP Sciences, Paris (2011)
Schmidt, E.: Zur theorie der linearen und nichtlinearen Integralgleichungen. Math. Ann. 63, 161 (1907)
Plenio, M.B., Virmani, S.: An introduction to entanglement measures. Quant. Inf. Comput. 7, 1–51 (2005)
Hugenholtz, N.M.: Physica 23, 481 (1957)
Kubo, R.: J. Math. Phys. 4, 174 (1963)
Wichmann, E.H., Crichton, J.H.: Phys. Rev. 132, 2788 (1983)
Weinberg, S.: The Quantum Theory of Fields I, Chapter 4. Cambridge University Press, Cambridge (2011)
Faddeev, L.D., Merkuriev, S.P.: Quantum Scattering Theory for Several Particle Systems. Springer, Berlin (1993)
Zurek, W.H.: Quantum Darwinism. Nat. Phys. 5, 181 (2009)
Brown, L.S.: Quantum Field Theory. Cambridge University Press, Cambridge (1992)
Hörmander, L.: The Analysis of Linear Partial Differential Operators. Springer, Berlin (1985)
Godement, R.: Topologie algébrique et théorie des faisceaux. Hermann, Paris (1973)
Lifshitz, E.M., Pitaevskii, L.P.: Physical Kinetics. Pergamon, London (1981)
Dautray, R., Lions, J.-L.: Mathematical Analysis and Numerical Methods for Science and Technology. Evolution Problems, I, II. Springer, Berlin (2000)
Wigner, E.P.: Interpretation of quantum mechanics. Am. J. Phys. 31, 6 (1963)
Joos, E., Zeh, H.D., Kiefer, C., Giulini, D., Kupsch, K., Stamatescu, I.O.: Decoherence and the Appearance of a Classical World in Quantum Theory. Springer, Berlin (2003)
Omnès, R.: A quantum approach to the uniqueness of Reality. In: Agazzi, E. (ed.) Turing’s Legacy, Proceedings of the meeting in September 2012 of the International Academy of Philosophy of Science, FranceAngeli, Milano (2013). arxiv.org/quant.phys/1302.1750
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Omnès, R. (2015). Local Properties, Growth and Transport of Entanglement. In: Blanchard, P., Fröhlich, J. (eds) The Message of Quantum Science. Lecture Notes in Physics, vol 899. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46422-9_11
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DOI: https://doi.org/10.1007/978-3-662-46422-9_11
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