Interaction in quantum communication

IEEE Transactions on Information Theory

Volumn 53, Issue 6, 2007, Pages 1970-1982

  Klauck, Hartmut ^a   Nayak, Ashwin ^b,c   Ta Shma, Ammon ^d   Zuckerman, David ^e  

^a GOETHE UNIVERSITY   (Germany)

^b UNIVERSITY OF WATERLOO   (Canada)

^c PERIMETER INSTITUTE FOR THEORETICAL PHYSICS   (Canada)

^d TEL AVIV UNIVERSITY   (Israel)

^e University of Texas at Austin   (United States)

Author keywords

Average encoding theorem; Entanglement assisted communication; Hellinger distance; Informational distance; Pointer jumping; Quantum communication complexity; Quantum information theory; Round complexity; Round reduction; Set disjointness

Indexed keywords

INFORMATION THEORY; MESSAGE PASSING; NETWORK PROTOCOLS;

AVERAGE ENCODING THEOREM; ENTANGLEMENT-ASSISTED COMMUNICATION; HELLINGER DISTANCE; QUANTUM COMMUNICATION COMPLEXITY;

QUANTUM THEORY;

EID: 34249860380     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2007.896888     Document Type: Article

References (39)

1. H. Buhrman, R. Cleve, and A. Wigderson, "Quantum vs. classical communication and computation" in Proc. 30th Annu. ACM Symp. Theory of Computing, Dallas, TX, May 1998, pp. 63-68.
2. A. Ambainis, L. J. Schulman, A. Ta-Shma, U. Vazirani, and A. Wigderson, "The quantum communication complexity of sampling" SIAM J. Comput. vol. 32, no. 6, pp. 1570-1585, 2003.
3. R. Raz, "Exponential separation of quantum and classical communication complexity," in Proc 31st Annu. ACM Symp. Theory of Computing, Atlanta, GA, May 1999, pp. 358-367.
4. A. Kitaev and J. Watrous, "Parallelization, amplification, and exponential time simulation of quantum interactive proof systems," in Proc. 32nd Annu. ACM Symp. Theory of Computing, Portland, OR, May 2000, pp 608-617.
5. C. H. Papadimitriou and M. Sipser, "Communication complexity," in Proc. 4th Annu. ACM Symp. Theory of Computing, San Francisco, CA, May 1982, pp. 196-200.
6. P. Duris, Z. Galil, and G. Schnitger, "Lower bounds on communication complexity," Inf. Computat., vol. 73, no. 1, pp. 1-22, 1987.
7. N. Nisan and A. Wigderson, "Rounds in communication complexity revisited," SIAM J. Comput., vol. 22, no. 1, pp. 211-219, 1993.
8. H. Klauck, "Lower bounds for computation with limited nondeterminism," in Proc. 13th Annu IFEE Conf. Computational Complexity, Buffalo, NY, Jun. 1998, pic 141-153.
9. S. J. Ponzio, J. Radhakrishnan, and S. Venkatesh, "The communication complexity of pointer chasing, applications of entropy and sampling," in Proc. 31st Annu. ACM Symp. Theory of Computing, Atlanta, GA, May 1999, pp. 602-611.
10. P. B. Miltersen, N. Nisan, S. Safra, and A. Wigderson, "On data structures and asymmetric communication complexity," in Proc. 27th Annu. ACM Symp. Theory of Computing, Las Vegas, NV, May/Jun. 1995, pp. 103-111.
11. H. Klauck, A. Nayak, A. Ta-Shma, and D. Zuckerman, "Interaction in quantum communication and the complexity of set disjointness," in Proc 33rd Annu. ACM Symp. Theory of Computing, Heraklion, Crete, Greece, Jul. 2001, pp. 124-133.
12. H. Buhrman and R. de Wolf, "Communication complexity lower bounds by polynomials," in Proc. 16th Annu. IEEE Conf. Computational Complexity, Chicago, IL, Jun. 2001, pp. 120-130.
13. A. Nayak, "Optimal lower bounds for quantum automata and random access codes," In Proc 40th Annu. IEEE Symp. Foundations of Computer Science, New York, NY, Oct. 1999, pp. 369-376.
14. A. Ambainis, A. Nayak, A. Ta-Shma and U. Vazirani, "Dense quantum coding and quantum finite automata," J. ACM, vol. 49, no. 4, pp. 1-16, Jul. 2002.
15. R. Cleve, W. van Dam, M. Nielsen, and A. Tapp, "Quantum entanglement and the communication complexity of the inner product function," in QCQS: Proc. NASA Int. Conf. Quantum Computing and Quantum Communications (Lecture Notes in Computer Science). Berlin: Germany, 1998, pp. 61-74.
16. C. H. Bennett and S. J. Wiesner, "Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states," Phys. Rev. Lett., vol. 69, pp. 2881-2884, 1992.
17. J. Preskill, Lecture Notes, 1998 [Online]. Available: http://www.theory.caltech.edu/people/preskill/ph229/
18. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information. Cambridge, U. K.: Cambridge Uni. Press, 2000.
19. A. A. Razborov, "Quantum communication complexity of symmetric predicates," Izv. Russian Acad. Sci., Mathematics, vol. 67, pp. 145-159, 2003, see also: Quant-ph/0204025.
20. S. Aaronson and A. Ambainis, "Quantum search of spatial regions," Theory of Computing, vol. 1, pp. 47-79, 2005.
21. R. Jain, J. Radhakrishnan, and P. Sen, "A lower bound for bounded round quantum communication complexity of set disjointness," in Proc 44th Annu. IEEE Symp. Foundations of Computer Science, 2003, pp. 220-229, see also quant-ph/0303138.
22. R. Jain, J. Radhakrishnan, and P. Sen, "The quantum communication complexity of the pointer chasing problem: The bit version," in Proceedings of the 22nd Conference on Foundations of Software Technology and Theoretical Computer Science, 2002, pp. 218-229.
23. R. Jain, J. Radhakrishnan, and P. Sen, "Privacy, and interaction in quantum communication complexity and a theorem about the relative entropy of quantum states," in Proceedings of the 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002, pp. 429-438.
24. S. Venkatesh and P. Sen, "Lower bounds in quantum cell probe model," in Proceedings of the 28th International Colloquium on Automata, Languages, and Programming, 2001, pp. 358-369, see also cs.CC/030903.
25. H. Klauck, "Quantum and approximate privacy," Theory of Computing Systems, vol. 37, pp. 221-246, 2004.
26. A. Chakrabarti and O. Regev, "An optimal randomised cell probe lower bound for approximate nearest neighbour searching," in Proc. 45th Annu. IEEE Symp. Fundations of Computer Science, Rome, Italy, Oct. 2004, pp. 473-482.
27. R. Jozsa, "Fidelity for mixed quantum states," J. Mod. Opt., vol. 41, no. 12, pp. 2315-2323, 1994.
28. A. Uhlmann, "The 'transition probability' in the state space of a *-algebra," Reports on Mathematical Physics, vol. 9, pp. 273-279, 1976.
29. C. A. Fuchs and J. van de Graaf, "Cryptographic distinguishability measures for quantum-mechanical states" IEEE Trans. Inf. Theory, vol. 45, no. 4, pp. 1216-1227, May 1999.
30. H. Lo and H. Chau, "Why quantum bit commitment and ideal quantum coin tossing are impossible," Physica D, vol. 120, pp. 177-187, 1998, see also quant-ph/9711065.
31. D. Mayers, "Unconditionally secure quantum bit commitment is impossible," Phys. Rev. Lett., vol. 78, pp. 3414-3417, 1997.
32. T. M. Cover and J. A. Thomas, Elements of Information Theory, ser. Wiley Series in Telecommunications. New York: Wiley, 1991.
33. M. Ohya and D. Petz, Quantum Entropy and its Use, ser. Texts and Monograph in Physics, 2nd ed. Heidelberg, Germany: Springer-Verlag, 1993, 2nd ed., 2004.
34. D. Dacunha-Castelle, "Vitesse de convergence pour certains problèmes statistiques," in Ecole d'Eté de Probabilités de Saint-Flour VII-1977, 1978, vol 678, Lecture Notes in Mathematics, pp. 1-172.
35. A. C.-C. Yao, "Quantum circuit complexity," in Proc. 34th Annu. IEEE Symp. Foundations of Computer Science, Palo, Alto, CA, Nov. 1993, pp. 352-361.
36. E. Kushilevitz and N. Nisan, Communication Complexity. Cambridge, U.K.: Cambridge Univ. Press, 1997.
37. E. Maneva, "Interactive Communication on Noisy Channels," B.S. thesis, Calif. Inst. Technol., Pasadena, 2001.
38. P. Sen, "Lower bounds for predecessor searching in the cell probe model," in Proc. 18th Annu. IEEE Conf. Computational Complexity (Complexity 2003), Aarhus, Denmark, Jul. 2003, pp. 73-83.
39. H. Klauck, "On quantum and probabilistic communication: Las vegas and one-way protocols," in Proc. 32nd Annu. ACM Symp. Theory of Computing, Portland, OR, May 2000, pp. 644-651.