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

TL;DR

This paper proposes a quantum simulation experiment using hypothetical closed timelike curves to demonstrate a nonclassical advantage in quantum metrology, surpassing classical limits through entanglement and effective time travel.

Contribution

It introduces a novel quantum simulation method to explore nonclassical advantages in metrology using hypothetical closed timelike curves and entanglement.

Findings

Entanglement enables information gain exceeding classical limits.

Simulated closed timelike curves can probabilistically improve metrological precision.

Operational advantages are demonstrated through a thought experiment involving effective time travel.

Abstract

We construct a metrology experiment in which the metrologist can sometimes amend her input state by simulating a closed timelike curve, a worldline that travels backward in time. The existence of closed timelike curves is hypothetical. Nevertheless, they can be simulated probabilistically by quantum-teleportation circuits. We leverage such simulations to pinpoint a counterintuitive nonclassical advantage achievable with entanglement. Our experiment echoes a common information-processing task: A metrologist must prepare probes to input into an unknown quantum interaction. The goal is to infer as much information per probe as possible. If the input is optimal, the information gained per probe can exceed any value achievable classically. The problem is that, only after the interaction does the metrologist learn which input would have been optimal. The metrologist can attempt to change her input by effectively teleporting the optimal input back in time, via entanglement manipulation. The effective time travel sometimes fails but ensures that, summed over trials, the metrologist's winnings are positive. Our Gedankenexperiment demonstrates that entanglement can generate operational advantages forbidden in classical chronology-respecting theories.