Geodesic
Mathematical structures related to the description of quantum states
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 501 (2021), pp. 57-61

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Some representations of states of quantum systems are discussed, and their equivalence is proved. In particular, an approach going back to L.D. Landau in which the density operator is constructed using a reduction of a pure state of a quantum system described by the tensor product of suitable Hilbert spaces is presented. Under these assumptions, changes in the states of subsystems of a quantum system caused by experiments are investigated.
Keywords: pure state, density operator, tensor product, reduction of states, Bell vector. 
@article{DANMA_2021_501_a10,
     author = {V. V. Kozlov and O. G. Smolyanov},
     title = {Mathematical structures related to the description of quantum states},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {57--61},
     publisher = {mathdoc},
     volume = {501},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_501_a10/}
}
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V. V. Kozlov; O. G. Smolyanov. Mathematical structures related to the description of quantum states. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 501 (2021), pp. 57-61. http://geodesic.mathdoc.fr/item/DANMA_2021_501_a10/