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We construct a metrology experiment in which the metrologist can sometimesamend her input state by simulating a closed timelike curve, a worldline thattravels backward in time. The existence of closed timelike curves ishypothetical. Nevertheless, they can be simulated probabilistically byquantum-teleportation circuits. We leverage such simulations to pinpoint acounterintuitive nonclassical advantage achievable with entanglement. Ourexperiment echoes a common information-processing task: A metrologist mustprepare probes to input into an unknown quantum interaction. The goal is toinfer as much information per probe as possible. If the input is optimal, theinformation gained per probe can exceed any value achievable classically. Theproblem is that, only after the interaction does the metrologist learn whichinput would have been optimal. The metrologist can attempt to change her inputby effectively teleporting the optimal input back in time, via entanglementmanipulation. The effective time travel sometimes fails but ensures that,summed over trials, the metrologist's winnings are positive. OurGedankenexperiment demonstrates that entanglement can generate operationaladvantages forbidden in classical chronology-respecting theories.

Nonclassical advantage in metrology established via quantum simulations of hypothetical closed timelike curves