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.Comment: 5+1 pages. 2 figures. Comments are welcomed