Canonical decompositions of n-qubit quantum computations and concurrence

Journal of Mathematical Physics

Volumn 45, Issue 6, 2004, Pages 2447-2467

  Bullock, Stephen S ^a   Brennen, Gavin K ^a  

^a NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2942675041     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1723701     Document Type: Article

References (27)

1. Barnum, H., and Linden, N., "Monotones and invariants for multi-particle quantum states," J. Phys. A 34, 6787-6805 (2001).
2. Bennett, C. H., DiVincenzo, D. P., Smolin, A., and Wooters, W. K., "Mixed state entanglement and quantum error correction," Phys. Rev. A 54, 3824-3851 (1996).
3. Bremner, M., Dodd, J., Nielsen, M., and Bacon, D., "Fungible dynamics: There are only two types of entangling multi-qubit interactions," Phys. Rev. A 69, 012313 (2004).
4. Bullock, S., and Markov, I., "An elementary two-qubit quantum computation in twenty-three elementary gates," Phys. Rev. A 68, 012318 (2003).
5. Eggeling, T., and Werner, R. F., "Separability properties of tripartite states with U×U×U symmetry," Phys. Rev. A 63, 042111 (2001).
6. Eisert, J., and Briegel, H., "The Schmidt measure as a tool for quantifying multi-particle entanglement," Phys. Rev. A 64, 022306 (2001).
7. Golub, G., and Loan, C. V., Matrix Computations (Johns Hopkins Press, Baltimore, 1996).
8. Helgason, S., Differential Geometry, Lie Groups, and Symmetric Spaces (American Mathematical Society, Providence, RI, Graduate studies in mathematics (corrected reprint of the 1978 original edition), 2001), Vol. 34.
9. Hill, S., and Wootters, W., "Entanglement of a pair of quantum bits," Phys. Rev. Lett. 78, 5022-5025 (1997).
10. Khaneja, N., Brockett, R., and Glaser, S. J., "Time optimal control in spin systems," Phys. Rev. A 63, 032308 (2001).
11. Knapp, A. Lie Groups Beyond an Introduction, Progress in Mathematics (Birkhäuser, Basel, 1996), Vol. 140.
12. Krauss, K., States, Effects, and Operations (Springer-Verlag, Berlin, 1983).
13. Krauss, B., and Cirac, J. I., "Optimal creation of entanglement using a two-qubit gate," Phys. Rev. A 63, 062309 (2001).
14. Lewenstein, M., Krauss, B., Horodecki, P., and Cirac, I., "Characterization of separable states and entanglement," Phys. Rev. A 63, 044304 (2001).
15. Makhlin, Y., "Nonlocal properties of two-qubit gates and mixed states and optimization of quantum computations," Quantum Inf. Process. 1, 243-252 (2002).
16. Meyer, D. A., and Wallach, N. R., "Global entanglement in multi-partite systems," J. Math. Phys. 43, 4273-4278 (2002).
17. Miyake, A., and Wadati, M., "Multi-partite entanglement and hyperdeterminants," Quantum Inf. Comput. 2, 540-555 (2002).
18. Nielsen, M., and Chuang, I., Quantum Information and Computation (Cambridge University Press, Cambridge, 2000).
19. Rungta, P., Buzek, V., Caves, C., Hillery, M., and Milburn, G., "Universal state inversion and concurrence in arbitrary dimensions," Phys. Rev. A 64, 042315 (2001).
20. Shende, V., Bullock, S., and Markov, I., "Recognizing small-circuit structure in two-qubit operators," quant-ph/0308045.
21. Tucci, R. A., "Rudimentary quantum compiler," quant-ph/9902062.
22. Uhlmann, A., "Fidelity and concurrence of conjugated states," Phys. Rev. A 62, 032307 (2000).
23. Vidal, G., "Entanglement monotones," J. Mod. Opt. 47, 355-376 (2000).
24. Vidal, G., and Dawson, C., "A universal quantum circuit for two-qubit transformations with three CNOT gates," Phys. Rev. A 69, 010301 (2004).
25. Wong, A., and Christensen, N., "Potential multiparticle entanglement measure," Phys. Rev. A 63, 044301 (2001).
26. Zhang, J., Vala, J., Sastry, S., and Whaley, K., "Geometric theory of nonlocal two-qubit operations," Phys. Rev. A 67, 042313 (2003).
27. n in the present paper will suppose that is not the case.