Nonclassical Advantage in Metrology Established via Quantum Simulations of Hypothetical Closed Timelike Curves

We construct a metrology experiment in which the metrologist can sometimes amend the 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 the 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.

Figure 1

Examples of chronology-violating particles traversing hypothetical CTCs. ${\rho }_{\mathrm{cv}}$ denotes such particles’ states. Time $t$, experienced by a chronology-respecting observer, runs from bottom to top. The time-traveling particle experiences time $T$. (a) Closed loop. (b) ${\rho }_{\mathrm{cv}}$ returns to its past and then travels forward in time again. (c) CTC interpretation of the successful trials of our Gedankenexperiment. ${\rho }_{\mathrm{cv}}$ is created at $T_1$ and travels forward in time until $T_2$. Then, it reverses temporal direction and travels backward in time until reaching $T_3$. After that, it again travels forward in time. ${\rho }_{\mathrm{cv}}$ then interacts with a chronology-respecting state, ${\rho }_{\mathrm{cr}}$, and is subsequently destroyed, prior to ${\rho }_{\mathrm{cv}}$’s creation ($T_1$). For comparison, the inset (d) depicts the standard teleportation, across space, of a quantum state needed as input for an interaction.

Figure 2

Circuit diagrams for (a) standard and (b) PCTC-powered weak-value amplification. Time progresses in the laboratory’s rest frame as one proceeds upward along the central, vertical axis. Black lines represent qubits. Dashed gray lines represent classical information.