Quantum Measurement Theory of Wormhole Length in Holography

We initiate the study of quantum measurement theory in holographic quantum gravity. As a concrete example, we calculate the quantum statistics of measuring the length of a wormhole in Jackiw-Teitelboim (JT) gravity and its nearly dual conformal field theory, the Sachdev-Ye-Kitaev (SYK) model. Two types of wormhole length measurements that can be implemented on experimental quantum simulators include: projective measurements in a digital superconducting qubit system, and continuous measurements in an analog cold atom cavity. In the former, we derive predictions for the variance in the wormhole length at finite N. In the latter, we calculate the wormhole standard quantum limit (SQL) and demonstrate that the act of measurement stabilizes its length. These results not only provide testable predictions for experimental simulations of holography, but also a foyer into how quantum measurements work in holographic theories.