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Mat. Zametki, 2013, Volume 93, Issue 3, Pages 323–332 (Mi mz9085)  

This article is cited in 1 scientific paper (total in 1 paper)

On Analogs of Spectral Decomposition of a Quantum State

G. G. Amosovab, V. Zh. Sakbaevab

a Steklov Mathematical Institute, Russian Academy of Sciences
b Moscow Institute of Physics and Technology (State University)

Abstract: The set of quantum states in a Hilbert space is considered. The structure of the set of extreme points of the set of states is investigated and an arbitrary state is represented as the Pettis integral over a finitely additive measure on the set of vector states, which is a generalization of the spectral decomposition of a normal state.

Keywords: quantum state, spectral decomposition, finitely additive measure.

Funding Agency Grant Number
Russian Foundation for Basic Research 09-01-00265
10-01-00395
Ministry of Education and Science of the Russian Federation 2.1.1/11133
2.1.1/12136


DOI: https://doi.org/10.4213/mzm9085

Full text: PDF file (500 kB)
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English version:
Mathematical Notes, 2013, 93:3, 351–359

Bibliographic databases:

UDC: 517.946+517.98
Received: 21.03.2011
Revised: 18.06.2012

Citation: G. G. Amosov, V. Zh. Sakbaev, “On Analogs of Spectral Decomposition of a Quantum State”, Mat. Zametki, 93:3 (2013), 323–332; Math. Notes, 93:3 (2013), 351–359

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. G. G. Amosov, V. Zh. Sakbaev, “Geometric properties of systems of vector states and expansion of states in Pettis integrals”, St. Petersburg Math. J., 27:4 (2016), 589–597  mathnet  crossref  mathscinet  isi  elib  elib
  • Математические заметки Mathematical Notes
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