Cryptographie distinguishability measures for quantum-mechanical states

IEEE Transactions on Information Theory

Volumn 45, Issue 4, 1999, Pages 1216-1227

  Fuchs, Christopher A ^a   Van Graaf, Jeroen De ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Bhattacharyya coefficient; Distinguishability of quantum states; Exponential indistinguishability; Kolmogorov distance; Probability of error; Quantum cryptography; Shannon distinguishability

Indexed keywords

ERRORS; PATTERN RECOGNITION; PROBABILITY DISTRIBUTIONS; QUANTUM THEORY; STATISTICAL METHODS;

BHATTACHARYYA COEFFICIENT; KOLMOGOROV DISTANCE; QUANTUM CRYPTOGRAPHY; SHANNON DISTINGUISHABILITY;

CRYPTOGRAPHY;

EID: 0032667067     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.761271     Document Type: Article

References (32)

1. E. Biham, M. Boyer, G. Brassard, J. van de Graaf, and T. Mor Security of quantum key distribution against all collective attacks," Tech. Rep. 9801022, LANL Quant-ph archives, 1998. [Online]. Available: http://xxx.lanl.gov/ps/quant-ph/9801022.
2. S. Goldwasser, S. Micali, and C. Rackoff The knowledge complexity of interactive proof-systems," SIAM. J. CompuL, vol. 18, no. 1, pp. 186-208, 1989.
3. D. Beaver Secure multiparty protocols and zero-knowledge proof systems tolerating a faulty minority," J. Cryptol., vol. 4, no. 2, pp. 75-122, 1991.
4. C. A. Fuchs Distinguishability and accessible information in quantum theory," Ph.D. dissertation, University of New Mexico, Albuquerque, 1995.
5. C. H. Bennett, T. Mor, and J. Smolin The parity bit in quantum cryptography," Phys. Rev. A. vol. 54, no. 3, p. 2675, 1996. [Online]. Available: http://xxx.lanl.gov/ps/quant-ph/9604040.
6. R. I. G. Hughes, The Structure and Interpretation of Quantum Mechanics. Boston, MA: Harvard Univ. Press, 1989.
7. C. Isham, Lectures on Quantum Theory. London, U.K.: Imperial College Press, 1995.
8. G. Brassard, C. Crépeau, R. Jozsa, and D. Langlois A quantum bit commitment scheme provably unbreakable by both parties," in Proc. 34th IEEE Symp. Foundations of Computer Science, 1993, pp. 362-371.
9. Sudbery, Quantum Mechanics and the Particles of Nature-An Outline for Mathematicians. Cambridge, U.K.: Cambridge Univ. Press, 1986.
10. A. Peres, Quantum Theory: Concepts and Methods. Dordrecht, The Netherlands: Kluwer, 1993.
11. N. D. Mermin The Ithaca interpretation of quantum mechanics," Tech. Rep. 9609013, LANL Quant-ph Archives, 1996 [Online]. Available: http://xxx.lanl.gov/ps/quant-ph/9609013.
12. M. Ben-Bassat Use of distance measures, information measures and error bounds in feature evaluation," in Handbook of Statistics, Vol.
13. Classification, Pattern Recognition and Reduction of Dimensionality, P. R. Krishnaiah and L. N. Kanal, Eds. Amsterdam, The Netherlands: North-Holland, 1982, pp. 773-791.
14. C. W. Heistrom, Quantum Detection and Estimation Theory (Mathematics in Science and Engineering), vol. 123. New York: Academic, 1976.
15. C. A. Fuchs Information Gain vs. State Disturbance in Quantum Theory," Fort. Phys., vol. 46, pp. 535-565, 1998.
16. A. C.-C. Yao Protocols for secure computations," in Proc. 23rd IEEE Symp. Foundations of Computer Science (Chicago, IL, 1982), pp. 160-164.
17. S. Goldwasser and S. Micali Probabilistic encryption," J. Comput. Syst. Sei, vol. 28, no. 2, pp. 270-299, 1984.
18. G. T. Toussaint Comments on 'The divergence and Bhattacharyya distance measures in signal selection'," IEEE Trans. Commun. Technol., vol. COM-20, p. 485, 1972.
19. M. Reed and B. Simon, Methods of Modern Mathematical Physics-Part I: Functional Analysis. New York: Academic, 1972.
20. A. Orlowski Measures of distance between quantum states," in Proc. 4th Workshop Physics and Computation-PhysComp '96 (New England Complex Systems Institute, Boston, MA, 1996), pp. 239-242.
21. T. Kailath The divergence and Bhattacharyya distance measures in signal selection," IEEE Trans. Commun. Technol., vol. COM-15, no. 1, pp. 52-60, 1967.
22. G. T. Toussaint Some functional lower bounds on the expected divergence for multihypothesis pattern recognition, communication, and radar systems," IEEE Trans. Syst., Man, Cybern., vol. SMC-1, pp. 384-385, 1971.
23. C. A. Fuchs and C. M. Caves Mathematical techniques for quantum communication theory," Open Syst. Inform. Dynamics, vol. 3, no. 3, pp. 345-356, 1995.
24. A. Uhlmann The 'transition probability' in the state space of a-algebra," Reps. Math. Phys., vol. 9, pp. 273-279, 1976.
25. R. Jozsa Fidelity for mixed quantum states," J. Modern Opt., vol. 41, no. 12, pp. 2315-2323, 1994.
26. C. E. Shannon A mathematical theory of communication," Bell Syst. Tech. J., vol. 27, pp. 379-423 and 623-656, 1948.
27. D. V. Lindley On a measure of the information provided by an experiment," Ann. Math. Statist., vol. 27, pp. 986-1005, 1956.
28. C. A. Fuchs and C. M. Caves Ensemble-dependent bounds for accessible information in quantum mechanics," Phys. Rev. Lett., vol. 73, no. 23, pp. 3047-3050, 1994.
29. T. Mor Quantum memory in quantum cryptography," Ph.D. dissertation, Technion-Israel Inst. Technol., Haifa, Israel, 1997.
30. M. E. Hellman and J. Raviv Probability of error, equivocation, and the Chernoff bound," IEEE Trans. Inform. Theory, vol. IT-16, pp. 368-372, July 1970.
31. T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley Series in Telecommunications). New York: Wiley, 1991.
32. C. H. Bennett and G. Brassard Quantum cryptography: Public key distribution and coin tossing," in Proc. IEEE Int. Conf. Computers, Systems and Signal Processing (Bangalore, India, 1984), pp. 175-179.