Optimal Asymmetric Quantum Cloning
Abstract
While the nocloning theorem, which forbids the perfect copying of quantum states, is wellknown as one of the defining features of quantum mechanics, the question of how well the theory allows a state to be cloned is yet to be completely solved. In this paper, rigorous solutions to the problem of M to N asymmetric cloning of qudits are obtained in a number of interesting cases. The central result is the solution to the 1 to N universal asymmetric qudit cloning problem for which the exact tradeoff in the fidelities of the clones for every N and d is derived. Analogous results are proven for qubits when M=N1. We also consider statedependent 1 to N qubit cloning, providing a general parametrization in terms of a Heisenberg star Hamiltonian. In all instances, we determine the feasibility of implementing the cloning economically, i.e., without an ancilla, and determine the dimension of the ancilla when an economic implementation is not possible.
 Publication:

arXiv eprints
 Pub Date:
 August 2012
 DOI:
 10.48550/arXiv.1208.5574
 arXiv:
 arXiv:1208.5574
 Bibcode:
 2012arXiv1208.5574K
 Keywords:

 Quantum Physics
 EPrint:
 12 pages