Todd A. Brun, Mark M. Wilde, Andreas Winter
We show that it is possible to clone quantum states to arbitrary accuracy in the presence of a Deutschian closed timelike curve (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 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 Deutschian CTCs.
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http://arxiv.org/abs/1306.1795
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