Quantum cloning machines and the applications

Abstract

No-cloning theorem is fundamental for quantum mechanics and for quantum information science that states an unknown quantum state cannot be cloned perfectly. However, we can try to clone a quantum state approximately with the optimal fidelity, or instead, we can try to clone it perfectly with the largest probability. Thus various quantum cloning machines have been designed for different quantum information protocols. Specifically, quantum cloning machines can be designed to analyze the security of quantum key distribution protocols such as BB84 protocol, six-state protocol, B92 protocol and their generalizations. Some well-known quantum cloning machines include universal quantum cloning machine, phase-covariant cloning machine, the asymmetric quantum cloning machine and the probabilistic quantum cloning machine etc. In the past years, much progress has been made in studying quantum cloning machines and their applications and implementations, both theoretically and experimentally. In this review, we will give a complete description of those important developments about quantum cloning and some related topics. On the other hand, this review is self-consistent, and in particular, we try to present some detailed formulations so that further study can be taken based on those results.

Group-representation approach to1→Nuniversal quantum cloning machines

“…In general, the subject was studied intensively, both for symmetric (all fidelities are equal) Universal Quantum Cloning Machines (UQCM) [4][5][6][7][8], and asymmetric (unequal fidelities) UQCM [8][9][10][11][12][13][14][15][16]. See also [17,18] for reviews. Nevertheless, for a long time there was a 'gap' in studies of quantum cloning -there was no general results on an admissible region of fidelities for universal asymmetric 1 → N quantum cloning machines.…”

Approximate broadcasting of quantum correlations

“…⊓ ⊔ Remark It is interesting that the optimal unilocal 2-broadcasting channel of the maximally entangled state is the same as the UQCM which comes from the global broadcasting setting. There is much progress on quantum cloning machine that has been made in the past years (see, e.g., [53,54]). For d⊗d bipartite maximally entangled state, its optimal unilocal 2-broadcasting channel is denoted as Υ d A→A1A2 with Choi matrix (16) and…”

Quantum cloning disturbed by thermal Davies environment

“…, the cloning machine U clon is universal (UQCM) [3,8]. In the paper, we assumes only these values for υ 1 , υ 2 and υ 3 .…”

“…The thermal noise, given here by the Davies map D[·], essentially affects both the states which arrives to Bob and information gained by Eve. We qualify [8] the effect of cloning by its fidelities given in Eq. (8): F Bob = F 2 in the case of Bob and F Eve = F 3 in the case of Eve.…”

“…Possibility of quantum cloning, even though imperfect, has a great impact on security of quantum data transmission [5,6]. References [7] and [8] can serve as two examples of reviews summarizing theoretical and practical achievements of quantum cloning.…”