Quantum state cloning using Deutschian closed timelike curves

TL;DR

This paper demonstrates that quantum states can be cloned with arbitrary accuracy using Deutschian closed timelike curves, effectively turning quantum mechanics into a classical theory within this model.

Contribution

It provides a scheme for perfect cloning of quantum states with D-CTCs and shows that D-CTCs make quantum mechanics effectively classical.

Findings

Quantum states can be cloned arbitrarily accurately with D-CTCs.

D-CTCs enable implementation of any continuous nonlinear map from states to states.

Deutsch's model renders quantum states perfectly distinguishable, making the theory effectively classical.

Abstract

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.