Making good codes for classical-quantum channel coding via quantum hypothesis testing

IEEE Transactions on Information Theory

Volumn 53, Issue 6, 2007, Pages 2261-2266

  Ogawa, Tomohiro ^a   Nagaoka, Hiroshi ^b  

^a JAPAN SCIENCE AND TECHNOLOGY AGENCY   (Japan)

^b UNIVERSITY OF ELECTRO COMMUNICATIONS   (Japan)

Author keywords

Classical capacity of quantum channels; Classical quantum channel coding; Quantum hypothesis testing; Quantum relative entropy

Indexed keywords

CODING ERRORS; ERROR CORRECTION; QUANTUM THEORY;

CLASSICAL-QUANTUM CHANNEL CODING THEOREM; HOLEVO-SCHUMACHER-WESTMORELAND (HSW) THEOREM; QUANTUM RELATIVE ENTROPY;

CHANNEL CODING;

EID: 34249788693     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2007.896874     Document Type: Article

References (23)

1. A.S. Holevo, "The capacity of the quantum channel with general signal states," IEEE Trans. Inf. Theory, vol. 44, pp. 269-273, 1998.
2. B. Schumacher and M. D. Westmoreland, "Sending classical information via noisy quantum channels," Phys. Rev. A, vol. 56, no. 1, pp. 131-138, 1997.
3. A.S. Holevo, "Some estimates for information quantity transmittes by quantum communication channels," Prob. Inf. Transm., vol. 9, no. 3, pp. 177-183, 1973.
4. P. Hausladen, R. Jozsa, B. Schumacher, M.D. Westmoreland, and W. K. Wootters, "Classical information capacity of a quantum channel," Phys. Rev. A, vol. 54, no. 3, pp. 1869-1876, 1996.
5. A. Winter, "Coding theorem and strong converse for quantum channels," IEEE Trans. Inf. Theory, vol. 45, pp. 2481-2485, 1999.
6. J. Wolfowitz, "The coding of messages sunject to chance errors," Illinois J. Math., pp. 591-606, 1957.
7. I. Csiszár and J. Körner, Information Theory, Coding Theorems for Discrete Memoryless Systems. Budapest, Hungary: Academic Press, 1981.
8. A.S. Holevo, "On the capacity of quantum communication channel," Prob. Inf. Transm., vol. 15, no. 4, pp. 247-253, 1979.
9. T. Ogawa and M. Hayashi, "On error exponents in quantum hypothesis testing," IEEE Trans. Inf. Theory, vol. 50, pp. 1368-1372, 2004.
10. M. Hayashi, "Optimal sequence of quantum measurements in the sense of Stein's lamma in quantum hypothesis testing," J. Phys. A: Math. Gen. vol. 50, pp. 10759-10773, 2002.
11. A. Feinstein, "A new basic theorem of information theory," IRE Trans. PGIT, vol. 4, pp. 2-22, 1954.
12. D. Blackwell, L. Breiman, and A. J. Thomasian, "The capacity of a class of channels," Ann. Math. Stat., vol. 30, pp. 1229-1241, 1959.
13. R. B. Ash, Information Theory. New York: Dover, 1965.
14. T. S. Han, Information-Spectrum Methods in Information Theory. New York:SPringer, 2002.
15. R. E. Blahut, Principles and Practice of Information Theory. Reading, MA: Addison-Wesley, 1991.
16. C. W. Helstrom, Quantum Detection and Estimation Theory. New York: Academic, 1976.
17. S. Verdú and T.S. Han, "A general formula for channel capacity," IEEE Trans. Inf. Theory, vol. 40, pp. 1147-1157, 1994.
18. T. Ogawa and H. Nagaoka, "A new proof of the channel coding theorem via hypothesis testing in quantum information theory," in Proc. IEEE Int. Symp. Inf. Theory, Lausanne, Switzerland, Jul. 2002, p. 73.
19. T. Ogawa, "A Study on the Asymptotic Property of the Hypothesis Testing and the Channel Coding in Quantum Mechanical Systems," (in Japanese) Ph.D. dissertation, University of Electro-Communications,, 2000.
20. M. Hayashi and H. Nagaoka, "General formulas for capacity of classical-quantum channels," IEEE Trans. Inf. Theory, vol 49, pp. 1753-1768, 2003.
21. A. Fujiwara and H. Nagaoka, "Operational capacity and pseudoclasicality of a quantum channel," IEEE Trans. Inf. Theory, vol 44, pp. 1071-1086, 1998.
22. F. Hiai and D. Petz, "The proper formula for relative entropy and its asymptotics in quantum probability," Commun. Math Phys., vol. 143, pp. 99-114, 1991.
23. T. Ogawa and H. Nagaoka, "Strong converse and Stein's lemma in quantum hypothesis testing," IEEE Trans. Inf. Theory, vol. 46, pp. 2428-2433, 2000.