利用Deutschian封闭类时曲线克隆量子态
Quantum state cloning using Deutschian closed timelike curves
摘要：
我们证明，在Deutschian封闭类时曲线（D-CTC）的存在下，克隆量子态到任意精度是可能的，随着CTC系统的维数变大，保真度在极限下收敛到1--从而解决了来自[Brun et al.，Physical Review Letters 102，210402（2009）]。这个结果来自于D-CTC辅助的方案，用于产生在已知本征基中制备的量子态的完美克隆，以及人们可以从信息完整测量的概率的经验估计重建量子态的近似的事实。我们的研究结果意味着更一般的是，每个连续的，但在其他任意非线性映射从状态到状态可以实现任意精度的D-CTC。此外，我们的研究结果表明，Deutsch的CTC模型实际上是一个经典的模型，在这个意义上，两个任意的，不同的密度算子是完全可区分的（在一个大的CTC系统的限制），因此，在这个模型中，量子力学成为一个经典的理论，其中每个密度算子是一个独特的点在一个经典的相空间。
英文摘要：
We show that it is possible to clone quantum states to arbitrary accuracy in the presence of a Deutschian closed timelike curve (D-CTC), with a fidelity converging to one in the limit as the dimension of the CTC system becomes large---thus resolving an open conjecture from [Brun et al., Physical Review Letters 102, 210402 (2009)]. This result follows from a D-CTC-assisted scheme for producing perfect clones of a quantum state prepared in a known eigenbasis, and the fact that one can reconstruct an approximation of a quantum state from empirical estimates of the probabilities of an informationally-complete measurement. Our results imply more generally that every continuous, but otherwise arbitrarily non-linear map from states to states can be implemented to arbitrary accuracy with D-CTCs. Furthermore, our results show that Deutsch's model for CTCs is in fact a classical model, in the sense that two arbitrary, distinct density operators are perfectly distinguishable (in the limit of a large CTC system); hence, in this model quantum mechanics becomes a classical theory in which each density operator is a distinct point in a classical phase space.
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