Optimal Universal Cloning of Mixed States

Yang Shuai, Meisheng Zhao, Nai-Le Liu +1 more

We present a series of universal quantum cloning machines for two identical mixed qubits. Every machine is optimal in the sense that it achieves the optimal bound of the single copy shrinking factor. Unlike in the case of pure state cloning, the single copy shrinking factor does not uniquely determine the cloning map in the case of mixed state cloning.

J.G. Gardiner, Jean-François S. Van Huele

Gui-Fang Dang, Heng Fan

The $N$ to $M$ $(M\ensuremath{\geqslant}N)$ universal quantum broadcasting of mixed states ${\ensuremath{\rho}}^{\ensuremath{\bigotimes}N}$ is proposed for a qubit system. The broadcasting of mixed states is universal and optimal in the sense that the shrinking factor is independent of the input state and achieves the upper bound. The quantum broadcasting of mixed qubits is a generalization of the universal quantum cloning machine for identical pure input states. A pure state decomposition of the identical mixed qubits ${\ensuremath{\rho}}^{\ensuremath{\bigotimes}N}$ is obtained.

Vanessa Brzić, Dmitry Grinko, Michał Studziński +1 more

State cloning and state transposition are fundamental transformations that, despite being desirable, cannot be perfectly realised as a consequence of two distinct requirements of quantum theory: cloning is forbidden by linearity, while transposition is ruled out by complete positivity. In this work, we show that, in spite of these disparate conceptual restrictions, the best physically allowed realisation of both transformations arises from a single physical process described by an isometry, which simultaneously implements their best possible approximations. This complementary relation allows us to determine the exact quantum and private classical capacities of the universal symmetric $N\to N+K$ cloning channel in the fully general multicopy qudit setting, thereby closing the remaining gap in the quantum capacity problem for universal cloning. We provide an explicit circuit that simultaneously implements optimal pure-state $N\to K$ transposition and optimal $N\to N+K$ symmetric cloning, both attaining the same fidelity. Additionally, we prove that the optimal $N\to K$ pure-state transposition channel is unique and realised by an estimation strategy. We also obtain the optimal mixed-state $N\to 1$ transposition, and discuss its differences from its pure-state analogue.

Zhihua Guo, HuaiXin Cao, ShiXian Qu

Irina Ion, Iulia Ghiu

We analyze the output mixed states generated when the asymmetric cloners are applied on a pure two-qubit state. We investigate two kinds of cloners: (a) local [Formula: see text] optimal universal asymmetric cloning machines and (b) nonlocal [Formula: see text] optimal universal asymmetric cloning machines. In both cases we find analytical formulae of the geometric quantum discord of the two clones. Finally, we prove that the geometric quantum discord generated by the nonlocal asymmetric cloners is not smaller than the geometric quantum discord given by the local asymmetric cloners.