Extracting state purity of a large system with limited control

As superconducting quantum devices with a large number of qubits become feasible, they offer an avenue for quantum simulation of equally large systems. The extraction of global information, such as a state's purity or entropy, remains a challenging prospect, generally requiring independent control of each qubit. Here, we propose a method of extracting the purity with limited control, applied through multiplexed dispersive readout. We consider the required control fidelity, and scaling of the number of measurements with system size.