Quantum simulations of time travel can power nonclassical metrology

Gambling agencies forbid late bets, placed after the winning horse crosses the finish line. A time-traveling gambler could cheat the system. We construct a gamble that one can win by simulating time travel with experimentally feasible entanglement manipulation. Our gamble echoes a common metrology protocol: A gambler must prepare probes to input into a metrology experiment. The goal is to infer as much information per probe as possible about a parameter's value. If the input is optimal, the information gained per probe can exceed any value achievable classically. The gambler chooses the input state analogously to choosing a horse. However, only after the probes are measured does the gambler learn which input would have been optimal. The gambler can "place a late bet" by effectively teleporting the optimal input back in time, via entanglement manipulation. Our Gedankenexperiment demonstrates that not only true time travel, but even a simulation offers a quantum advantage in metrology.