TY - JOUR

T1 - On Errors Generated by Unitary Dynamics of Bipartite Quantum Systems

AU - Amosov, G. G.

AU - Mokeev, A. S.

N1 - Funding Information: The work is supported by Russian Science Foundation under the grant no. 19-11-00086 and performed in Steklov Mathematical Institute of Russian Academy of Sciences. Publisher Copyright: © 2020, Pleiades Publishing, Ltd. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2020/12

Y1 - 2020/12

N2 - Abstract: Given a quantum channel it is possible to define the non-commutative operator graph whose properties determine a possibility of error-free transmission of information via this channel. The corresponding graph has a straight definition through Kraus operators determining quantum errors. We are discussing the opposite problem of a proper definition of errors that some graph corresponds to. Taking into account that any graph is generated by some POVM we give a solution to such a problem by means of the Naimark dilatation theorem. Using our approach we construct errors corresponding to the graphs generated by unitary dynamics of bipartite quantum systems. The cases of POVMs on the circle group Zn and the additive group $$\mathbb{R}$$ are discussed. As an example we construct the graph corresponding to the errors generated by dynamics of two mode quantum oscillator.

AB - Abstract: Given a quantum channel it is possible to define the non-commutative operator graph whose properties determine a possibility of error-free transmission of information via this channel. The corresponding graph has a straight definition through Kraus operators determining quantum errors. We are discussing the opposite problem of a proper definition of errors that some graph corresponds to. Taking into account that any graph is generated by some POVM we give a solution to such a problem by means of the Naimark dilatation theorem. Using our approach we construct errors corresponding to the graphs generated by unitary dynamics of bipartite quantum systems. The cases of POVMs on the circle group Zn and the additive group $$\mathbb{R}$$ are discussed. As an example we construct the graph corresponding to the errors generated by dynamics of two mode quantum oscillator.

KW - covariant resolution of identity

KW - non-commutative operator graphs

KW - quantum anticliques

KW - symmetric Fock space

UR - http://www.scopus.com/inward/record.url?scp=85100579523&partnerID=8YFLogxK

U2 - 10.1134/S1995080220120069

DO - 10.1134/S1995080220120069

M3 - Article

AN - SCOPUS:85100579523

VL - 41

SP - 2310

EP - 2315

JO - Lobachevskii Journal of Mathematics

JF - Lobachevskii Journal of Mathematics

SN - 1995-0802

IS - 12

ER -