Optimum Testing of Multiple Hypotheses in Quantum Detection Theory

IEEE Transactions on Information Theory

Volumn 21, Issue 2, 1975, Pages 125-134

  Yuen, Horace P ^a   Kennedy, Robert S ^a   Lax, Melvin ^b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b LUCENT TECHNOLOGIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DECISION THEORY AND ANALYSIS; OPTICAL COMMUNICATION;

INFORMATION THEORY;

EID: 0016485946     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/TIT.1975.1055351     Document Type: Article

References (42)

1. A. Wald. Statistical Decision Functions. New York: Wiley, 1950.
2. D. Middleton, An Introduction to Statistical Communication Theory. New York: McGraw-Hill, 1960, ch. 23.
3. H. L. Van Trees, Detection, Estimation, and Modulation Theory: Part I. New York: Wiley, 1968, ch. 2.
4. C. W. Helstrom, “Detection theory and quantum mechanics,” Inform. Contr., vol. 10, pp. 254–291, Mar. 1967.
5. H. P. Yuen, “Communication theory of quantum systems,” Res. Lab. Electron., M.I.T., Cambridge, Mass., Tech. Rep. 482, Aug. 1971 (Ph.D. dissertation submitted to the Dep. Elec. Eng., M.I.T., June 1970), pp. 116–129.
6. H. P. Yuen, R. S., Kennedy, and M. Lax, “On optimal quantum receivers for digital signal detection,” Proc. IEEE (Lett.), vol. 58, pp. 177-1773, Oct. 1970.
7. E. B. Davies, “On the repeated measurement of continuous observables in quantum mechanics,” J. Functional Anal., vol. 6, pp. 318–346, 1970, see in particular pp. 340–343.
8. A. S. Holevo, “Statistical problems in quantum physics,” in Proc. Soviet-Japanese Symp. Probability and Statistics, vol. 1, 1972, pp. 22–40.
9. A. S. Holevo, “Statistical decision theory for quantum systems,” J. Multivariate Analysis, vol. 3, pp. 337–394, 1973.
10. A. S. Holevo, “Optimal quantum measurement,” (in Russian) Theoreticheskayer i Matematicheskaya Fizika, vol. 17, pp. 319–326, Dec. 1973.
11. J. Von Neumann, Mathematical Foundations of Quantum Mechanics. Princeton, N.J.: Princeton Univ. Press, 1955.
12. E. Prugovechi, Quantum Mechanics in Hilbert Space. New York: Academic, 1971.
13. s. K. Berberian, Notes on Spectral Theory. New York: Van Nostrand-Reinhold, 1966.
14. P. A. Benioff, “Operator valued measures in quantum mechanics: Finite and infinite processes,” J. Math. Phys., vol. 13, pp. 231–242, 1972.
15. C. W. Helstrom and R. S. Kennedy, “Noncommuting observables in quantum detection and estimation theory,” IEEE Trans. Inform. Theory, vol. IT-20, pp. 16–24, Jan. 1974.
16. H. P. Yuen and M. Lax, “Multiple parameter quantum estimation and measurement of nonselfadjoint observables,” IEEE Trans. Inform. Theory, vol. IT-19, pp. 740–750, Nov. 1973.
17. B. Sz-Nagy, “Transformations in Hilbert space which extend beyond this space,” Appendix to F. Riesz and B. Sz-Nagy, Functional Analysis. New York: Ungar, 1960.
18. E. Arthurs and J. L. Kelly, Jr., “On the simultaneous measurement of a pair of conjugate observables,” Bell Syst. Tech. J., (Briefs), vol. 44, pp. 725–729, Apr. 1965.
19. J. P. Gordon and W. H. Louisell, “Simultaneous measurements of noncommuting observables,” in Physics of Quantum Electronics, P.L. Kelly, B. Lax, and P. E. Tannenwald, Eds. New York: McGraw-Hill, 1966. pp. 833–840.
20. H. L. Royden, Real Analysis. New York: MacMillian, 1965.
21. O. L. Mangasarian, Nonlinear Programming. New York: McGraw-Hill, 1969.
22. J. W. S. Liu, “Reliability of quantum-mechanical communication systems,” Res. Lab. Electron., M.I.T., Cambridge, Mass., Tech. Rep. 468, Dec. 1968. See also IEEE Trans. Inform. Theory, vol. IT-16, pp. 319–329, May 1970.
23. R. S. Kennedy, Res. Lab. Electron., M.I.T., Cambridge, Mass., Q.P.R. 110, July 15, 1973, pp. 142-146.
24. D. G. Luenberger, Optimization by Vector Space Methods. New York: Wiley, 1969.
25. H. P. Yuen and M. Lax, “Multiple parameter quantum estimation with applications to radar and analog communications,” presented at IEEE Int. Symp. Information Theory, Asilomar, Calif., Jan. 31, 1972.
26. J. M. Wozencraft and I. M. Jacobs, Principles of Communication Engineering, New York: Wiley, 1965.
27. P. A. M. Dirac, The Principles of Quantum Mechanics, 4th ed. New York: Oxford Univ. Press, 1958.
28. R. J. Glauber, “Optical coherence and photon statistics,” in Quantum Optics and Electronics. C. M. De Witt et al., Eds. New York: Gordon and Breach, 1965.
29. J. R. Klauder and E. C. G. Sudarshan, Fundamentals of Quantum Optics. New York: Benjamin, 1968.
30. C. W. Helstrom, J. W. S. Liu, and J. P. Gordon, “Quantum. mechanical communication theory,” Proc. IEEE, vol. pp. 1578–1598, Oct. 1970.
31. R. S. Kennedy, Res. Lab. Electron, M.I.T., Cambridge, Mass., Q.P.R. 112, Jan. 1974.
32. A. J. Viterbi, Principles of Coherent Communication. NewYork: McGraw-Hill, 1966.
33. J. P. Gordon, “Quantum effects in communication systems,” Proc. IRE, vol. 50, pp. 1898–1908, Sept. 1962.
34. C. W. Helstrom, “Capacity of the pure-state quantum channel,” Proc. IEEE (Lett.), vol. 62, pp. 139–140, Jan. 1974.
35. J. N. Pierce, “Ultimate performance of M-ary transmissions on fading channels,” IEEE Trans. Inform. Theory, vol. IT-12, pp. 2–5, Jan. 1966.
36. R. M. Van Slyke and R.J. B. Wets, “A duality theory for abstract mathematical programs with applications to optimal control theory,” J. Math. Anal. Appl., vol. 22, pp. 679–706, 1968.
37. L. Hurwicz, “Programming in linear spaces,” in Studies in Linear and Nonlinear Programming, K. J. Arrow et al., Eds. Stanford, Calif., Stanford Univ. Press, 1958, pp. 38–102.
38. J. Horvath, Topological Vector Spaces and Distributions, vol. 1, Reading, Mass.: Addison-Wesley, 1966.
39. R. Schatten, Norm Ideals of Completely Continuous Operators. Berlin: Springer-Verlag, 1970.
40. I. M. Gelfand and N. Y. Vilenkin, Generalized Functions, vol. 4, New York: Academic, 1964.
41. S. T. Hu, Elements of General Topology. San Francisco: Holden-Day, 1964.
42. F. Riesz and B. Sz-Nagy, Functional Analysis. New York: Ungar, 1955.