Abstract: . . .  of multipar- tite asymmetric quantum cloning machines, and have illus- trated it with two examples. These devices have several re- markable properties. One of them is that if one wants to produce n clones from an input with a fidelity which is as high as possible, some quantum information still remains to produce a nontrivial n 훘 clone. Multipartite cloning ma- chines provide a new tool for analyzing the security of mul- tipartite quantum cryptography, and the trade-off between disturbance and information gain. We have presented fea- sible optical realizations of our examples of optimal multi- partite cloners. We have then seen that the noise that charac- terizes these cloning . . .
. . .  Other interesting limiting cases are F A , F B , F C = 1,1/2,1/2 when T 1 =1/2, while taking T 2 =1 gives Eqs. 7 for the 1 ? 1 case. This construction can easily be generalized further. In summary, we have introduced the concept of multipar- tite asymmetric quantum cloning machines, and have illus- trated it with two examples. These devices have several re- markable properties. One of them is that if one wants to produce n clones from an input with a fidelity which is as high as possible, some quantum information still remains to produce a nontrivial n 훘 clone. Multipartite cloning ma- . . .
. . .  acknowledge support from Grant No. MSM 6198959213 of the Czech Ministry of Education, and A.A. acknowledges support from the Spanish MCYT under “Ramón y Cajal” grant. 1 W. K. Wootters and W. H. Zurek, Nature London 299 , 802 1982 . 2 D. Dieks, Phys. Lett. 92 , 271 1982 ; N. Gisin, Phys. Lett. A 242 , 1 1998 . 3 J. Preskill, Quantum Information and Computation, Lecture Notes in Physics 1998 . 4 D. Bruss and C. Macchiavello, Phys. Lett. A 253 , 249 1999 . 5 N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74 , 145 2002 . 6 V. Buzek and M. Hillery, Phys. Rev. A 54 , 1844 1996 . 7 A. Lamas-Linares, C. Simon, J. C. Howell, and D. Bouw- meester, . . .
. . .  optical realizations of our examples of optimal multi- partite cloners. We have then seen that the noise that charac- terizes these cloning machines is related to the unavoidable spontaneous emission that necessarily accompanies stimu- lated emission. One is tempted to conjecture that all the N ?M 1 ¯ M P cloning machines for qubits are only limited by spontaneous emission, and can therefore be implemented by splitting and then recombining the clones and anticlones produced by stimulated emission using a series of beam splitters, in a similar way as in Fig. 1. The corresponding fidelities would define the optimal distribution of a qubit among several . . .
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