Mathematical Structures Related
to the Description of Quantum States
Academician of the RAS V. V. Kozlova,* and O. G. Smolyanovb,**
a Steklov Mathematical Institute, Russian Academy
of Sciences, Moscow, 119991 Russia
b Faculty of Mechanics and Mathematics,
Lomonosov Moscow State University, Moscow, 119991 Russia
Correspondence to: *e-mail: kozlov@pran.ru
Correspondence to: **e-mail: smolyanov@yandex.ru
Received 8 November, 2021
Abstract—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
DOI: 10.1134/S1064562421060119