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Mat. Zametki, 2013, Volume 93, Issue 5, Pages 775–789 (Mi mz10234)  

This article is cited in 2 scientific papers (total in 2 papers)

Schmidt Number and Partially Entanglement-Breaking Channels in Infinite-Dimensional Quantum Systems

M. E. Shirokov

Steklov Mathematical Institute of the Russian Academy of Sciences

Abstract: The Schmidt number of a state of an infinite-dimensional composite quantum system is defined and several properties of the corresponding Schmidt classes are considered. It is shown that there are states with given Schmidt number such that any of their countable convex decompositions does not contain pure states of finite Schmidt rank. The classes of infinite-dimensional partially entanglement-breaking channels are considered, and generalizations of several properties of such channels, which were obtained earlier in the finite-dimensional case, are proved. At the same time, it is shown that there are partially entanglement-breaking channels (in particular, entanglement-breaking channels) such that all of their operators in any Kraus representation are of infinite rank.

Keywords: Schmidt number, Schmidt rank, composite quantum system, quantum channel, Schmidt decomposition, entanglement, partially entanglement-breaking channels.

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Russian Foundation for Basic Research 12-01-00319-а
13-01-00295-а


DOI: https://doi.org/10.4213/mzm10234

Full text: PDF file (600 kB)
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English version:
Mathematical Notes, 2013, 93:5, 766–779

Bibliographic databases:

UDC: 519.248.3
Received: 15.11.2011

Citation: M. E. Shirokov, “Schmidt Number and Partially Entanglement-Breaking Channels in Infinite-Dimensional Quantum Systems”, Mat. Zametki, 93:5 (2013), 775–789; Math. Notes, 93:5 (2013), 766–779

Citation in format AMSBIB
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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. Li X., Fang X., “Constructing K-Schmidt Witnesses For Infinite-Dimensional Systems”, Linear Multilinear Algebra, 63:4 (2015), 754–764  crossref  mathscinet  zmath  isi
    2. Namiki R., “Schmidt-number benchmarks for continuous-variable quantum devices”, Phys. Rev. A, 93:5 (2016), 052336  crossref  isi  scopus
  • Математические заметки Mathematical Notes
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