Publication: Sequential Implementation of Global Quantum Operations
Loading...
Full text at PDC
Publication Date
2008-10-31
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
American Physical Society
Citations
Exportar
Abstract
We study the possibility for a global unitary applied on an arbitrary number of qubits to be decomposed in a sequential unitary procedure, where an ancillary system is allowed to interact only once with each qubit. We prove that sequential unitary decompositions are in general impossible for genuine entangling operations, even with an infinite-dimensional ancilla, being the controlled-NOT gate a paradigmatic example. Nevertheless, we find particular nontrivial operations in quantum information that can be performed in a sequential unitary manner, as is the case of quantum error correction and quantum cloning.
Description
UCM subjects
Unesco subjects
Keywords
Citation
M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).
V. Scarani, S. Iblisdir, N. Gisin, and A. Acın, Rev. Mod. Phys. 77, 1225 (2005).
J. Preskill Quantum information and computation edited by H.-K. Lo, S. Popescu, and T. P. Spiller (World Scientific, Singapore, 1998).
D. Deutsch, Proc. R. Soc. A 400, 97 (1985).
C. Schön, E. Solano, F. Verstraete, J. I. Cirac, and M. M. Wolf, Phys. Rev. Lett. 95, 110503 (2005).
C. Schön, K. Hammerer, M.M. Wolf, J. I. Cirac, and E. Solano, Phys. Rev. A 75, 032311 (2007).
D. Pérez-García, F. Verstraete, M. M. Wolf, and J. I. Cirac, Quantum Inf. Comput. 7, 401 (2007).
M. Fannes, B. Nachtergaele, and R. F. Werner, Commun. Math. Phys. 144, 443 (1992).
G. Vidal, Phys. Rev. Lett. 91, 147902 (2003).
F. Verstraete, D. Porras, and J. I. Cirac, Phys. Rev. Lett. 93,227205 (2004).
T. Wilk, S. C. Webster, A. Kuhn, and G. Rempe, Science 317, 488 (2007).
H. Christ, J. I. Cirac, and G. Giedke, arXiv:0710.4120.
Y. Delgado, L. Lamata, J. Leo´n, D. Salgado, and E. Solano, Phys. Rev. Lett. 98, 150502 (2007).
R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. 86, 5188 (2001).
P. Shor, Phys. Rev. A 52, R2493 (1995).
Note that one could implement any full N ! N unitary if the following protocol were allowed: (i) we map locally the chain qubits onto blank ancilla qubits, (ii) we apply locally the desired global unitary on the ancilla qubits,(iii) we map back locally the ancilla qubits onto their corresponding chain qubits. However, it is clear that this recipe breaks the sequential condition.
R. A. Horn and C. R. Johnson, Topics in Matrix Analysis (Cambridge University Press, Cambridge, 1991).
V. Buzek and M. Hillery, Phys. Rev. A 54, 1844 (1996).
W. K. Wootters and W. H. Zurek, Nature (London) 299, 802 (1982).
N. Gisin and S. Massar, Phys. Rev. Lett. 79, 2153 (1997).