Eur. Phys. J. D 65, 621-625 (2011)
https://doi.org/10.1140/epjd/e2011-20370-2

Optimal asymmetric 1 → 4 quantum cloning in arbitrary dimension

¹ School of Physics and Electronics, Henan University, Kaifeng 475001, P.R. China
² Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100080, P.R. China

e-mail: renxijun@mail.ustc.edu.cn

Received: 22 June 2011
Received in final form: 13 September 2011
Published online: 28 October 2011

Abstract

We present an optimal asymmetric 1 → 4 quantum cloner. Our derivation generalizes the constructions of optimal asymmetric 1 → 2 and 1 → 3 quantum cloners in [Quantum Inf. Comput 5, 583 (2005)]. We explicitly prove the optimality of this cloner and give the maximum achievable fidelities. We also present the relation between the optimal quantum cloner with the multipartite entangled state which shows the singlet monogamy inequality in [Phys. Rev. Lett. 103, 050501 (2009)].