Nonlocal Hamiltonian simulation assisted by local operations and classical communications

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 66, Issue 2, 2002, Pages

  Vidal, G ^a   Cirac, J I ^a  

^a UNIVERSITY OF INNSBRUCK   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; GROUND STATE; HAMILTONIANS; NUMERICAL METHODS; OPTIMIZATION;

LOCAL OPERATIONS AND CLASSICAL COMMUNICATION; NONLOCAL HAMILTONIAN SIMULATION;

QUANTUM THEORY;

EID: 0036701630     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. W. Dür, G. Vidal, J.I. Cirac, N. Linden, and S. Popescu, Phys. Rev. Lett. 87, 137901 (2001).
2. J.L. Dodd, M.A. Nielsen, M.J. Bremner, and R.T. Thew, Phys. Rev. A 65, 040301(R) (2002).
3. P. Wocjan, D. Janzing, and Th. Beth, e-print quant-ph/0106077.
4. C.H. Bennett, J.I. Cirac, M.S. Leifer, D.W. Leung, N. Linden, S. Popescu, and G. Vidal, Phys. Rev. A 66, 012305 (2002).
5. P. Wocjan, R. Rotteller, D. Janzing, and T. Beth, Quantum Information and Computation 2, 133 (2002).
6. M.A. Nielsen, M.J. Bremner, J.L. Dodd, A.M. Childs, and C.M. Dawson, e-print quant-ph/0109064.
7. P. Wocjan, M. Rotteller, D. Janzing, and T. Beth, e-print quant-ph/0109088.
8. A.G. Butkovskiy and Y.L. Samoilenko, Control of Quantum Mechanical Processes and Systems (Kluwer Academic, Dordrecht), 1990.
9. C. P. Slichter, Principles of Magnetic Resonance (Springer, Berlin). 1996.
10. W. Dür, G. Vidal, and J.I. Cirac, e-print quant-ph/0112124.
11. In this work we assume that local ancillary systems are available at wish in LO protocols (see Sec. III), and thus we make no distinction between LO and LO+anc. (as opposed to Ref. [4]).
12. -ikτ′H′|ψ> for k=1,2,...,N. Perfect dynamics simulation corresponds to taking the large N limit.
13. iH′T′ by H′ and LU, G. Vidal, K. Hammerer, and J.I. Cirac, Phys. Rev. Lett. 88, 237902 (2002).
14. B can be added and removed by means of local unitary operations, and thus we can safely omit them in the present argumentation.
15. R. Bhatia, Matrix Analysis (Springer-Verlag, New York, 1997).
16. G. Vidal, D. Jonathan, and M.A. Nielsen, Phys. Rev. A 62, 012304 (2000).
17. One can use the results of Ref. [16], concerning the robustness of entanglement transformations under a pertubation of the state under consideration, to show that the argument of Sec. III B 2 of this paper is also robust under O(t) modifications of a maximally entangled state.
18. P.M. Alberti and A. Uhlmann, Stochasticity and Partial Order: Doubly Stochastic Maps and Unitary Mixing (Dordrecht, Boston). 1982.
19. Herbert J. Bernstein (private communication), has obtained, independently, a similar majorization-based proof of the necessary conditions for efficient simulation of two-qubit Hamiltonians.
20. G. Vidal and I. Cirac, Phys. Rev. Lett. 88, 167903 (2002).