Quantum t-designs: T-wise independence in the quantum world

Proceedings of the Annual IEEE Conference on Computational Complexity

Volumn , Issue , 2007, Pages 129-140

  Ambainis, Andris ^a   Emerson, Joseph ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; GRAPH THEORY; PROBLEM SOLVING; RANDOM VARIABLES; SET THEORY; STATE SPACE METHODS;

DERANDOMIZATION; FINITE SETS; QUANTUM STATES; STATE-DISTINCTION PROBLEM;

QUANTUM COMPUTERS;

EID: 34748892553     PISSN: 10930159     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CCC.2007.26     Document Type: Conference Paper

References (21)

1. N. Alon, L. Babai, A. Itai. A fast and simple algorithm for the maximal independent set problem. Journal of Algorithms, 7:567-583, 1986.
2. B. Bajnok. Construction of spherical t-designs. Geom. Dedicata, 43:167-179, 1992.
3. H. Barnum. Information-disturbance tradeoff in quantum measurement on the uniform ensemble and on the mutually unbiased bases. ArXiv.org Preprint quant-ph/0205155, 2002.
4. B. Berger. The fourth moment method. SIAM Journal on Computing, 26:1188-1207, 1997.
5. C. Danker, R. Cleve, J. Emerson, E. Livine. Exact and Approximate Unitary 2-designs: Constructions and Applications, quant-ph/0606161.
6. P. Delsarte, J. Goethals, J. Seidel. Spherical codes and designs. Geom. Dedicata, 6:363-388, 1977.
7. R. Hamming. Numerical methods for scientists and engineers. McGraw-Hill, 1966.
8. P. Hayden, D. Leung, P. Shor, A. Winter. Randomizing quantum states: Constructions and applications. Commun. Math. Phys., 250(2):371-391, 2004. quant-ph/0307104.
9. A. Hayashi, T. Hashimoto, M. Horibe. Reexamination of optimal quantum state estimation of pure states. Phys. Rev. A, 72: 032325, 2006. Also quant-ph/0410207.
10. S. Iblisdir, J. Roland. Optimal finite measurements and Gauss quadratures. Phys. Lett. A, 358(5-6):368-372, 2006. Also quant-ph/0410237.
11. Andreas Klappenecker and Martin Roetteler. Mutually unbiased bases are complex projective 2-designs. ArXiv.org Preprint quant-ph/0502031, 2005.
12. Andreas Klappenecker, Martin Roetteler, Igor E. Shparlinski, and Arne Winterhof, On Approximately Symmetric Informationally Complete Positive Operator-Valued Measures and Related Systems of Quantum States, quant-ph/0503239.
13. J. Korevaar, J. Meyers. Chebyshev-type quadrature on multidimensional domains. Journal of Approximation Theory, 79:144-164, 1994.
14. G. Kuperberg. Numerical cubature using error-correcting codes. SIAM Journal on Numerical Analysis, 44:897-907, 2006.
15. G. Kuperberg. Numerical cubature from Archimedes' hat-box theorem. SIAM Journal on Numerical Analysis, 44:908-935, 2006.
16. J. Naor, M. Naor, Small-bias probability spaces: Efficient constructions and applications, SIAM J. Computing, 22: 838-856, 1993.
17. J. Radhakrishnan, M. Rotteler, P. Sen, On the power of random bases in Fourier sampling, ICALP'05 and quant-ph/0503114.
18. J. Renes, R. Blume-Kohout, A. Scott, C. Caves, J. Math. Phys. 45(6):2171-2180 (2004).
19. P. Sen, Random measurement bases, quantum state distinction and applications to the hidden subgroup problem, Complexity'06 and quant-ph/0512085.
20. N. Ullah, Nucl. Phys. 58:65, 1964.
21. D. Zuckerman. Lecture notes for CS 395T - Pseudorandomness and Combinatorial Constructions (Spring 2001), http://www.es.utexas.edu/users/diz/ 395T/01/, Lecture 5.