No Access

A Markov–Dobrushin Inequality for Quantum Channels

Luigi Accardi

Centro Vito Volterra, Università di Roma “Tor Vergata”, Roma I-00133, Italy

E-mail Address: accardi@volterra.uniroma2.it

Search for more papers by this author

Yun Gang Lu

Dipartimento di Matematica, Università di Bari, via Orabona, 4, 70125 Bari, Italy

E-mail Address: yungang.lu@uniba.it

Search for more papers by this author

, and

Abdessatar Souissi

Department of Accounting, College of Business Management, Qassim University, Buraidah 52571, Saudi Arabia

Preparatory Institute for Scientific and Technical Studies La Marsa, Carthage University, Tunisia

LR18ES45, Mathematical Physics, Quantum Modeling and Mechanical Design, University of Carthage, Carthage, Tunisia

E-mail Address: a.souaissi@qu.edu.sa

Search for more papers by this author

https://doi.org/10.1142/S1230161221500189Cited by:6 (Source: Crossref)

Abstract

We propose a quantum extension of the Markov-Dobrushin inequality. As an application, we estimate the Markov-Dobrushin constant for some classes of quantum Markov channels, in particular for the Pauli channel, widely studied in quantum information theory.

Keywords:

References

1. L. Accardi , Func. Anal. Appl. 9, 1 (1975). Crossref, Google Scholar
2. L. Accardi , J. Math. Anal. Appl. 72, 1 (1979). Crossref, Web of Science, Google Scholar
3. L. Accardi, A. Souissi, and E.G. Soueidy , Infin. Dim. Analysis Quant. Probab. Rel. Top. 23, 2050016 (2020). Link, Web of Science, Google Scholar
4. L. Accardi , Phys. Rep. 77, 169 (1981). Crossref, Web of Science, Google Scholar
5. L. Accardi and F. Fidaleo , Annali di Matematica 184, 327 (2005). Crossref, Web of Science, Google Scholar
6. A.M. Childs, E. Farhi, and S. Gutmann , Quant. Inf. Process. 1, 35 (2002). Crossref, Web of Science, Google Scholar
7. R.L. Dobrushin , Theory Prob. Appl. 1, 65 (1956). Crossref, Google Scholar
8. R. Fagnola and R. Rebolledo , Infin. Dim. Analysis Quant. Probab. Rel. Top. 1, 561 (1998). Link, Web of Science, Google Scholar
9. S.C. Moy , Pacific J. Math. 4, 47 (1954). Crossref, Google Scholar
10. F. Mukhamedov and A. Al-Rawashdeh , Positivity 24, 855 (2020). Crossref, Web of Science, Google Scholar
11. F. Mukhamedov , J. Math. Anal. Appl. 408, 364 (2013). Crossref, Web of Science, Google Scholar
12. F. Mukhamedov , J. Phys.: Conf. Ser. 435, 012002 (2013). Crossref, Google Scholar
13. D.W. Robinson , Commun.Math. Phys. 19, 219 (1970). Crossref, Web of Science, Google Scholar
14. S. Sakai , C∗-algebras and W∗-algebras, Springer, 1971. Google Scholar
15. J. Tomiyama , Proc. Japan Acad. 33, 608 (1957). Crossref, Google Scholar
16. H. Umegaki , Tohoku Math. J. 6, 177 (1954). Crossref, Google Scholar
17. A. Yu. Veretennikov and M.A. Veretennikova, Izvestiya RAN , Seriya Matematicheskaya 86, (2022). (English edition: Izvestiya: Mathematics) Google Scholar