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Schmidt modes and entanglement

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Motivated by their frequent use in quantum mechanical studies of entanglement, we give a brief overview of Schmidt modes and Schmidt decompositions of two-particle wave functions. We discuss methods of their derivation and include a little-known approach used in the original work by E. Schmidt [Math. Annalen, 63 (1906), 433]. This employs the bipartite wave function itself rather than the more complicated two-party reduced density matrix. As an illustration, Schmidt modes for two-photon polarisation qutrits are derived in a general form. The derivation is accompanied by a series of simple examples with special choices of parameters. Relationships between Schmidt modes, polarisation Stokes vectors and entanglement are also discussed.

Keywords: Schmidt decomposition; Stokes vectors; biphoton; entanglement; qutrits

Document Type: Research Article


Affiliations: 1: A.M. Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow, Russia. 2: Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region, Russia.

Publication date: 2014-04-03

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