Theoretical Information Limits for a Quantum Entangled Network of Magnetometers

Distributed quantum sensing is expected to offer innovative paths to accelerate the development of time synchronization [1], sensing capabilities of gravity gradients and magnetic fields [2], and to advance the search of new physics, such as dark matter domain walls [3]. Classical networks vary widely in structure depending on their randomness, modularity, and heterogeneity. We study a tree network, where each node represents an individual magnetometer. The Fisher Information is then used to determine the maximum amount of information we can recover about one parameter from the measurements. For an electromagnetically induced transparency (EIT) magnetometer, we are interested in how small of a phase shift can be detected within a global homogeneous magnetic field. We then use the Cramer-Rao bound to determine the lowest limit in uncertainty of our measurements. We iterate this process for one single magnetometer, then a classical network followed by an entangled network. By comparing our results for both a classical and quantum network, entangled nodes are able to improve the uncertainty of our measurements by a factor scaling up to the square root of the number of nodes. By improving measurement sensitivity for a network of magnetometers, we aim to be able to detect increasingly small shifts in a magnetic field. The improvements gained by entangling a network have widespread applications, from quantum sensing to the search for exotic physics in the HEP community.